Branched polymers as viscosity and/or friction modifiers for lubricants

ABSTRACT

Embodiments of branched polymer lubricant additives comprise a branched polymer and, when combined with a lubricant base at a concentration from 1 wt % to 50 wt %, provide (i) a viscosity index ≧150, (ii) that is at least 10% less than a coefficient of friction of the lubricant base alone in contact with a component of a device during operation of the device at a temperature within a range of 20 to 100° C., or (iii) both (i) and (ii).

CROSS REFERENCE TO RELATED APPLICATION

This application claims the benefit of the earlier filing date of U.S. Provisional Application No. 62/035,802, filed Aug. 11, 2014, which is incorporated in its entirety herein by reference.

ACKNOWLEDGMENT OF GOVERNMENT SUPPORT

This invention was made with government support under DE-AC0576RLO1830 awarded by the U.S. Department of Energy. The government has certain rights in the invention.

FIELD

This disclosure concerns embodiments of a branched polymer that, when combined with a lubricant base at an effective concentration, provides an increased viscosity index and/or a reduced coefficient of friction compared to the lubricant base alone.

BACKGROUND

The main driving force behind the development of new lubricant additives is to meet ever increasing challenges towards fuel economy and environmental stewardship. Lubricant formulations include many additives to improve efficiency (e.g., by reducing friction) and prolong the life of mechanical components (i.e., reduce wear). It is widely accepted that fuel-saving engine oil formulations feature good viscosity index properties. In order to attain these properties, the engine oil must be designed to behave differently at high and low temperatures. At low temperatures, the viscosity of the oil must not become too high in the presence of additives as to prevent solidification of the oil. At high temperatures, the additives must resist the inherent thinning of the oil, as to prevent boundary friction and wear. Additives that promote low viscosity at low temperature but maintain sufficient viscosity at high temperatures are desirable for fuel economy.

The viscosity index (VI) number of an oil provides insight into the thinning effect (decrease in viscosity) of a lubricant formulation at temperatures of 40 and 100° C. (ASTM D2270). Ideally, the change in viscosity would be minimal between these temperatures, affording consistent lubricity. However, a natural thinning effect is observed at elevated temperatures, and polymeric additives provide an opportunity to minimize the loss in viscosity. This can be achieved by increasing the shear thickness (intermolecular interactions) of the polymer/oil blend and/or by a globular-to-coil transition (expansion) of the polymer in the oil between low to high temperatures (−20 to 150° C.).

SUMMARY

This disclosure concerns embodiments of branched polymers that are useful as lubricant additives to improve the viscosity index and/or reduce the coefficient of friction of a lubricant base (e.g., a hydrocarbon or synthetic oil).

In some embodiments, the branched polymer comprises (i) a hyperbranched polar core having a functionality of at least 3 and comprising a plurality of heteroatoms, and (ii) a plurality of polymeric or non-polymeric arms bonded to the hyperbranched polar core, wherein when the functionality is within a range of 3-21 and the plurality of arms is polymeric, the hyperbranched polar core is not a cyclotetrasiloxane derivative, a cyclophosphazene derivative, a calixarene derivative, a cyclodextrin derivative, or a saccharide derivative. In certain embodiments, the hyperbranched polar core is derived from a branched 2,2-bis(hydroxymethyl)propionic acid polyester comprising 8-256 hydroxy moieties, a branched polyethyleneimine comprising primary, secondary, and tertiary amine groups and having an weight average molecular weight within a range of 600-10,000 Daltons, or a branched polyamidoamine comprising 8-256 primary amine moieties. In one embodiment, each of the plurality of arms is a non-polymeric arm derived from a C₈-C₂₀ aliphatic carboxylic acid, a C₈-C₂₀ aliphatic acyl halide, a C₈-C₂₀ aliphatic ester, or a C₈-C₂₀ aliphatic glycidyl ether. In some embodiments, each of the plurality of arms is a random copolymer or a block copolymer, the random or block copolymer comprising first monomeric units derived from nonpolar monomers and second monomeric units derived from polar monomers. The random or block copolymer may be formed via atom-transfer radical polymerization. Suitable nonpolar monomers include unsubstituted alkenes, aryl-substituted alkenes wherein the aryl group is alkyl-substituted or unsubstituted, alkyl acrylates wherein the alkyl group of the alkyl acrylate is unsubstituted and has 6 to 20 carbon atoms, methacrylates wherein the alkyl group of the alkyl methacrylate is unsubstituted and has 6 to 20 carbon atoms, lipophilic vinyl monomers, or a combination thereof. In certain embodiments, each of the second monomeric units comprises at least one heteroatom. Exemplary polar monomers are

where t is an integer from 1 to 10, or a combination thereof.

In some embodiments, the branched polymer is a hyperbranched polymer comprising an aryl polyester core derived from AB_(x) monomers, AB_(x)+B_(y) monomers, or A₂+B_(y) monomers, where x≧2 and y≧3, and a plurality of polymeric or non-polymeric arms bonded to the aryl polyester core. In certain embodiments, the monomers are AB₂ monomers having a structure

where n is an integer from 3 to 20, and the core has a degree of branching within a range of 0.1 to 0.9. In one embodiment, the branched polymer includes a plurality of non-polymeric arms having a structure —(C(O)—(CH₂)_(q))— where q is an integer from 8 to 16. In an independent embodiment, the branched polymer includes a plurality of homopolymeric arms derived from a nonpolar monomer, wherein the nonpolar monomer is an unsubstituted alkene, an aryl-substituted alkene wherein the aryl group is alkyl-substituted or unsubstituted, an alkyl acrylate wherein the alkyl group of the alkyl acrylate is unsubstituted and has 6 to 20 carbon atoms, a methacrylate wherein the alkyl group of the alkyl methacrylate is unsubstituted and has 6 to 20 carbon atoms, or a lipophilic vinyl monomer. In yet another independent embodiment, the branched polymer comprises a plurality of copolymeric arms comprising first monomeric units derived from nonpolar monomers and second monomeric units derived from polar monomers, each second monomeric unit comprising at least one heteroatom. In certain examples, the first monomeric units are derived from ethylene and the second monomeric units are derived from polar monomers having a general formula R¹—C(O)O—R², wherein R¹ is an alkenyl moiety and R² is a C₁-C₃ alkyl moiety or a heteroaliphatic moiety including at least one oxygen atom, at least one nitrogen atom, or at least one oxygen atom and at least one nitrogen atom. Exemplary polar monomers include

where t is an integer from 1 to 10, or a combination thereof.

In some embodiments, the branched polymer is a branched polyolefin including first monomeric units derived from an olefin and second monomeric units derived from a polar monomer including at least one heteroatom, wherein if the olefin is ethylene, then the polar monomer is not an alkenyl ether, methyl-9-decenoate, or methyl 2,2-dimethylpent-4-enoate. In certain embodiments, the polar monomers comprise vinyl monomers, acrylate monomers, methacrylate monomers, or a combination thereof. In one embodiment, the polar monomers have a general formula R¹—C(O)O—R², wherein R¹ is an alkenyl moiety and R² is a short-chain alkyl moiety (e.g., 1-3 carbon atoms) or a heteroaliphatic moiety including at least one oxygen atom, at least one nitrogen atom, or at least one oxygen atom and at least one nitrogen atom.

The disclosed branched polymers are useful as lubricant additives. Embodiments of a lubricant include a lubricant base and a branched polymer that, when combined with a lubricant base at a concentration from 1 wt % to 50 wt %, (i) provides a viscosity index 150, (ii) has a coefficient of friction that is at least 10% less than a coefficient of friction of the lubricant base alone in contact with a component of a device during operation of the device at a temperature within a range of 20 to 100° C., or (iii) both (i) and (ii). The branched polymer is (a) a branched polymer comprising (i) a hyperbranched polar core having a functionality of at least 3 and comprising a plurality of heteroatoms, and (ii) a plurality of polymeric or non-polymeric arms bonded to the hyperbranched polar core, wherein when the functionality is within a range of 3-21 and the plurality of arms is polymeric, the hyperbranched polar core is not a cyclotetrasiloxane derivative, a cyclophosphazene derivative, a calixarene derivative, a cyclodextrin derivative, or a saccharide derivative; (b) a hyperbranched polymer comprising an aryl polyester core derived from monomers AB_(x) monomers, AB_(x)+B_(y) monomers, or A₂+B_(y) monomers, where x≧2 and y≧3, the aryl polyester core having a degree of branching within a range of 0.1 to 0.9, and a plurality of polymeric or non-polymeric arms bonded to the aryl polyester core; or (c)) a branched polyolefin comprising first monomeric units derived from an olefin and second monomeric units derived from a polar monomer including at least one heteroatom. In some embodiments, the lubricant includes 1 to 50 wt % of the branched polymer. In any or all of the above embodiments, the lubricant base may be a group I oil, group II oil, a group III oil, a group IV oil, a group V oil, or any combination thereof.

Embodiments of the disclosed lubricants are made by combining a lubricant base with a branched polymer as disclosed herein to form a lubricant as disclosed herein. Embodiments of the disclosed lubricants are useful for lubricating a device. For example, a method of lubricating an engine includes supplying to the engine a lubricant as disclosed herein.

The foregoing and other objects, features, and advantages of the disclosure will become more apparent from the following detailed description, which proceeds with reference to the accompanying figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows traditional schematic drawings of polymers with linear (a), ring (b), star (c), hyperbranched (d), and dendrimer (e) architectures.

FIG. 2 is a schematic drawing of an exemplary branched polymer that undergoes a conformational change as temperature changes.

FIG. 3 is a schematic drawing showing intermolecular interaction between two exemplary branched polymers.

FIGS. 4A and 4B are schematic drawings of exemplary hyperbranched polymers that are subsequently functionalized with lipophilic or copolymeric moieties to form branched polymer lubricant additives.

FIG. 5 is a chemical structure of an exemplary hyperbranched polymer prepared from an AB₂ monomer and post-modified with a lipophilic moiety.

FIG. 6 is a schematic drawing showing the effect of pressure during synthesis on topology of branched polyolefins.

FIG. 7 shows an exemplary synthetic scheme for preparing hyperbranched polymers comprising a hyperbranched polar core and a plurality of polymeric arms bound to the core.

FIG. 8 shows an exemplary synthetic scheme for preparing comb-burst, hyperbranched aryl polyesters.

FIG. 9 is a bar graph comparing kinematic viscosity values and respective viscosity indexes of controls, base oil, and several comb-burst, hyperbranched aryl polyesters. Viscosity data and index values were determined via a spindle viscometer. A standard 5% and 10% error was assigned to viscosity and viscosity index values, respectively.

FIG. 10 shows a Stribeck curve and illustrations of boundary lubrication, mixed lubrication, and hydrodynamic lubrication regimes.

FIGS. 11A-11C are Stribeck curves of 1.67 wt % Control 2 (11A), and 2 wt % of an exemplary comb-burst, hyperbranched aryl polyester (11B) at 23° C. (left panel) and 100° C. (right panel); 11C shows the reduction in friction coefficient achieved by subtracting the base oil friction.

FIG. 12 is a bar graph showing viscosity and viscosity index results from branched polyethylene homopolymers and copolymers including methyl-10-undecanoate monomeric units in a group III base oil.

FIGS. 13A-13D show friction measurements of a control lubricant (13A), a branched polyethylene homopolymer (13B), a branched polyethylene random copolymer including methyl-10-undecanoate monomeric units (13C), and a branched polyethylene block copolymer including methyl-10-undecanoate monomeric units (13D) in a group I base oil at 23° C.

FIGS. 14A-14D show friction measurements of a control lubricant (14A), a branched polyethylene homopolymer (14B), a branched polyethylene random copolymer including methyl-10-undecanoate monomeric units (14C), and a branched polyethylene block copolymer including methyl-10-undecanoate monomeric units (14D) in a group I base oil at 100° C.

DETAILED DESCRIPTION

Polymers constitute a significant portion of the conventional additives blended into lubricants and are utilized as viscosity index improvers (VIIs). The role of a VII is to mitigate viscosity changes that the lubricant experiences over operating temperatures (e.g. −20 to 150° C. for engine oils). Much emphasis has been placed on reducing the natural thinning effect that occurs at higher temperatures (40 to 150° C.). An ideal polymeric additive would have minimal influence on the lubricant's viscosity at low temperatures (−20 to 40° C.) and significantly reduce the natural thinning effect of the lubricant at elevated temperatures (40 to 150° C.). High-performing polymeric additives become even more imperative as original equipment manufacturers (OEMs) design engines that show significant fuel economy gains when utilizing low viscosity oils (e.g. SAE 0W-20). Sliding friction in an engine is significantly reduced by the addition of lubricants. There are three regimes of lubrication, depending on the thickness of the lubricating film between the moving parts: boundary lubrication, mixed lubrication and hydrodynamic lubrication. In an operating engine, all three regimes occur simultaneously in different parts of the engine although some dominate under different conditions of operation. Therefore, engine durability requires lubricant additives that help the oil to maintain a suitable viscosity at elevated temperatures as well as under mechanical shear. This disclosure concerns embodiments of branched polymers that are useful as lubricant additives to improve the viscosity index and/or reduce the coefficient of friction of a lubricant base (e.g., a hydrocarbon or synthetic oil). Methods of making and using the lubricants are also disclosed.

I. DEFINITIONS AND ABBREVIATIONS

The following explanations of terms and abbreviations are provided to better describe the present disclosure and to guide those of ordinary skill in the art in the practice of the present disclosure. As used herein, “comprising” means “including” and the singular forms “a” or “an” or “the” include plural references unless the context clearly dictates otherwise. The term “or” refers to a single element of stated alternative elements or a combination of two or more elements, unless the context clearly indicates otherwise.

Unless explained otherwise, all technical and scientific terms used herein have the same meaning as commonly understood to one of ordinary skill in the art to which this disclosure belongs. Although methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present disclosure, suitable methods and materials are described below. The materials, methods, and examples are illustrative only and not intended to be limiting. Other features of the disclosure are apparent from the following detailed description and the claims.

Unless otherwise indicated, all numbers expressing quantities of components, molecular weights, percentages, temperatures, times, and so forth, as used in the specification or claims are to be understood as being modified by the term “about.” Accordingly, unless otherwise implicitly or explicitly indicated, or unless the context if properly understood by a person of ordinary skill in the art to have a more definitive construction, the numerical parameters set forth are approximations that may depend on the desired properties sought and/or limits of detection under standard test conditions/methods as known to those of ordinary skill in the art. When directly and explicitly distinguishing embodiments from discussed prior art, the embodiment numbers are not approximates unless the word “about” is recited.

Definitions of common terms in chemistry may be found in Richard J. Lewis, Sr. (ed.), Hawley's Condensed Chemical Dictionary, published by John Wiley & Sons, Inc., 1997 (ISBN 0-471-29205-2) and other similar references.

In order to facilitate review of the various embodiments of the disclosure, the following explanations of specific terms are provided:

Acyl halide: A compound having the general formula R—C(O)—X, where R is alkyl, heteroalkyl, haloalkyl, aliphatic, heteroaliphatic, aryl, or heteroaryl, and X is halide (bromide, chloride, fluoride, or iodide).

Aliphatic: A substantially hydrocarbon-based compound, or a radical thereof (e.g., C₆H₁₃, for a hexane radical), including alkanes, alkenes, alkynes, including cyclic versions thereof, and further including straight- and branched-chain arrangements, and all stereo and position isomers as well. Unless expressly stated otherwise, an aliphatic group contains from one to twenty-five carbon atoms; for example, from one to fifteen, from one to ten, from one to six, or from one to four carbon atoms. The term “lower aliphatic” refers to an aliphatic group containing from one to ten carbon atoms. An aliphatic chain may be substituted or unsubstituted. Unless expressly referred to as an “unsubstituted aliphatic,” an aliphatic group can either be unsubstituted or substituted. An aliphatic group can be substituted with one or more substituents (up to two substituents for each methylene carbon in an aliphatic chain, or up to one substituent for each carbon of a —C═C— double bond in an aliphatic chain, or up to one substituent for a carbon of a terminal methine group). Exemplary substituents include, but are not limited to, alkoxy, alkylamino, alkylthio, acyl, aldehyde, amide, amino, aminoalkyl, aryl, carboxyl, cyano, cycloalkyl, dialkylamino, halo, haloaliphatic, heteroaliphatic, heteroaryl, heterocycloaliphatic, hydroxyl, oxo, sulfonamide, sulfhydryl, thioalkoxy, or other functionality.

Alkyl: A hydrocarbon group having a saturated carbon chain. The chain may be cyclic, branched or unbranched. The term lower alkyl means the chain includes 1-10 carbon atoms. The term alkenyl refers to hydrocarbon groups having carbon chains containing one or more double bonds.

Arm: As used herein, the term “arm” refers to (i) a long-chain (8-24 carbon atoms) aliphatic or heteroaliphatic molecule bound to a functional group on a core molecule, or (ii) a polymer bound to a functional group on a core molecule. A polymeric arm may be a homopolymer or a copolymer. A polymeric arm includes a plurality of monomeric units. In some embodiments, the polymeric arm includes at least 50 monomeric units.

Asperity: The term “asperity” refers to unevenness of surface, i.e., roughness. When generally smooth surfaces come into contact with one another, initial contact occurs at surface asperities. Friction and wear originate at these contact points.

ATRP: Atom-transfer radical polymerization. In ATRP, a transition metal compound is reacted with a compound having a transferable atom group. The transferable atom group is transferred to the transition metal compound, thereby oxidizing the metal and forming a free-radical compound. The free radical reacts with alkene groups, e.g., ethylenic groups. Because the transfer of the atom group to the transition metal compound is reversible, the atom group is transferred back to the growing polymer chain, which provides a controlled polymerization reaction. Due to a catalytic loading, equal or less than 5 mol %, of the transition metal, and an equilibrium that favors the transferable atom being attached to the terminus of the growing polymer, the propagating radical is disproportionately low, which reduces unwanted polymerization events and affords narrow distributions of targeted molecular weights with enhanced precision over chemical compositions. So called “controlled” polymerizations are considered to contain these latter attributes.

Carboxylic acid: A carbonyl-bearing functional group having a formula RCOOH where R is aliphatic, heteroaliphatic, alkyl, or heteroalkyl.

Coefficient of friction (COF): A dimensionless value describing the ratio of the force of friction between two bodies and the force pressing them together. COF may be represented by the Greek letter μ. As used herein, COF refers to kinetic (or sliding) coefficient of friction in which the surfaces are in relative motion.

Copolymer: A polymer formed from polymerization of two or more structurally different monomers. Simultaneous polymerization of two or more structurally different monomers generally produces a random copolymer (sometimes referred to as a statistical copolymer). Sequential polymerization of a first monomer followed by a second monomer produces a diblock block copolymer having a first series of monomeric units derived from the first monomers and a second series of monomeric units derived from the second monomers. Sequential polymerization is performed by adding a first monomer during the initial stages of polymerization, and then adding a subsequent monomer at a subsequent, later time (e.g., after a majority, or substantially all, of the first monomers have been incorporated into the polymer). Triblock (and higher) copolymers may be produced by sequential addition of subsequent monomers. A tapered block copolymer is obtained by sequential addition of two co-monomers, such that the first block contains a first monomer, an intermediate block includes both monomers, and a final block is primarily composed of the second monomer.

Core: As used herein, the term “core” refers to a branched or hyperbranched molecule comprising a plurality of functional groups and from which certain of the disclosed branched and hyperbranched polymers are derived. Typically the functional groups have the same composition. The functional groups may be symmetrically or unsymmetrically distributed on the core. A branched or hyperbranched polymer is produced by bonding a plurality of nonpolymeric or polymeric arms to the core via reaction with the functional groups of the core molecule.

Degree of branching (DOB): The term “degree of branching” refers to the number of branches per molecule and is provided as a value from 0-1 or a percentage. In some instances, when the polymer is not a branched polyolefin, percent DOB may be calculated as (T+Z)/(T+Z+L)×100, where T is the average number of terminally bonded monomer units, Z is the average number of monomer units forming branches, and L is the average number of linearly bonded monomer units. For branched polyolefins, DOB may be expressed as the number of branches per 1,000 carbon atoms.

Dendritic: A branching configuration in which branches increase exponentially extending from a starting point or core to the periphery. The configuration is highly defined. A dendritic polymer generally is symmetric around the core and may have a spherical, globular morphology.

Derivative: A molecule that differs in chemical structure from a parent or base compound, for example a structure that differs by one or more functional groups. As used herein, the term “derivative” refers to a molecule that has undergone a chemical reaction to become part of a larger molecule.

Derived from: As used herein, the term “derived from ‘xx’” means that ‘xx’ was a reactant and the chemical structure is altered in the product formed. For example, when a core having terminal hydroxyl moieties is reacted with molecules or monomers to produce arms bonded to the core, the hydroxy groups react with the molecules or monomers resulting in a polymer having a core that forms —O— linkages with the arms. Similarly, monomers used to form polymers may include an alkylene group prior to polymerization. During polymerization, the double bond is broken when the monomer forms bonds with adjacent monomers or a core molecule and an adjacent monomer. Thus, monomeric units in the polymer are “derived from” the monomers and no longer include the alkylene bond.

Dynamic (absolute) viscosity: A measure of internal resistance to shearing flows; the tangential force per unit area required to move one horizontal plane with respect to another plane, at a unit velocity, while maintaining a unit distance apart in the fluid. Dynamic viscosity is commonly expressed in centipoise (0.01 g/(cm·s), 0.001 N·s/m²).

Ester: A chemical compound derived from an organic acid (general formula: RCO₂H) where the hydrogen of the —OH (hydroxy) group is replaced by an aliphatic or aryl group. A general formula for an ester derived from an organic acid is shown below:

where R and R′ denote virtually any group, including aliphatic, substituted aliphatic, heteroaliphatic, substituted heteroaliphatic, aryl, heteroaryl, etc.

Functionality: As used herein with respect to a hyperbranched polymer comprising a core and a plurality of polymeric arms, the term “functionality” refers to the number of chemical bonds through which the core can be joined to the polymeric arms. For example, the core molecule 2,2-bis(hydroxymethyl)propionic acid polyester-16-hydroxyl has a functionality of 16.

Glycidyl ether: A functional group having the general structure:

HAPe: Hyperbranched aryl polyester

Heteroaliphatic: An aliphatic compound or group having at least one heteroatom, i.e., one or more carbon atoms has been replaced with an atom having at least one lone pair of electrons, typically nitrogen, oxygen, phosphorus, silicon, or sulfur. Heteroaliphatic compounds or groups may be substituted or unsubstituted, branched or unbranched, cyclic or acyclic, and include “heterocycle”, “heterocyclyl”, “heterocycloaliphatic”, or “heterocyclic” groups.

Heteroatom: As used herein, the term “heteroatom” refers to an atom, having at least one lone pair of electrons, which has replaced a carbon atom of an organic molecule or moiety. Typical heteroatoms are nitrogen, oxygen, sulfur, and phosphorus.

Homopolymer: A polymer in which all of the monomeric units have the same chemical structure. For example, a polyethylene homopolymer is comprised only of monomeric units derived from ethylene.

Hyperbranched polymer: As used herein, the term “hyperbranched polymer” refers to a nonlinear polymer having a degree of branching (DOB) per molecule of 0.4-1, such as 0.4≦DOB≦0.9, or a DOB from 40-90% (as defined above), a polymer with at least 100 branching points per 1000 carbons (including carbon atoms in the branches), or a polymer that contains at least one dendritic moiety.

Kinematic viscosity: The ratio of dynamic viscosity to density. Kinematic viscosity (Kv) is determined by dividing the dynamic viscosity (p) of a fluid by its mass density (p). Kv is commonly expressed in centistokes (cSt) where 1 cSt=10⁻⁶ m²/s or 1 mm²/s. Unless otherwise specified as “dynamic viscosity” or reported in units of centipoise, the term “viscosity” as used herein refers to “kinematic viscosity.”

Liphophilic: Groups or molecules which are hydrocarbon rich and tend to combine with or dissolve in lipids, e.g., oils, and nonpolar solvents. A homopolymer derived from lipophilic monomers and having a molecular weight of at least 100,000 g/mole has a solubility of at least 0.1 wt % at 0° C. in a paraffin-base mineral oil.

Lubricant: A substance capable of reducing friction between surfaces in mutual contact.

Lubricant additive—A compound that improves the lubricant performance of a base oil. Types of lubricant additives include detergent additives, corrosion or rust-inhibiting additives, antioxidant additives, metal deactivators, pour point depressants, extreme pressure agents, antiwear additives, dispersants, anti-foam agents, antimisting agents, additional viscosity index improvers, additional viscosity modifiers, and combinations thereof.

Lubricant base: As used here, the term “lubricant base” refers to the majority component of a lubricant composition. Lubricant bases include mineral oils (derived from crude oil), biolubricants (e.g., triglyceride esters derived from plants and animals), synthetic oils (e.g., polyalphaolefins, synthetic esters, polyalkylene glycols, alkylated naphthalenes), and combinations thereof.

Moderately branched polymer: As used herein, the term “moderately branched polymer” refers to a nonlinear branched polymer having a degree of branching (DOB) that is less than 40%, such as 0.1≦DOB<0.4, or 10%≦DOB<40%, or a polymer with a range of branches between 20 to 100 per 1000 carbon atoms.

Moiety: A fragment of a molecule.

Monomer: A molecule or compound (usually containing carbon) that can react and combine with other monomers (of the same or different chemical structure) to form polymers. For example, polystyrene is formed by polymerization of the monomer styrene. Common monomers include, for example and without limitation, alkenes, amides, unsaturated carboxylic acids, and unsaturated aliphatic esters.

Number average molecular weight: The statistical average molecular weight of all the polymer chains in a sample, defined as:

${Mn} = \frac{\Sigma \; N_{i}M_{i}}{\Sigma \; N_{i}}$

where M_(i) is the molecular weight of a chain, and N_(i) is the number of chains of that molecular weight. M_(n) can be predicted by polymerization mechanisms and is measured by methods that determine the number of molecules in a sample of a given weight, e.g., gel permeation chromatography, viscometry, colligative methods such as vapor pressure osmometry, end group assays, or proton NMR. When used in general statements (e.g., “comparable molecular weights”), the term “molecular weight” as used herein with respect to a polymer may refer to either of the number average molecular weight or the weight average molecular weight. When used in a specific context, the molecular weight is expressly stated as number average or weight average molecular weight.

Olefin: An unsaturated, acyclic aliphatic hydrocarbon having one or more double bonds. Olefins with one double bond are alkenes. A polyolefin is a polymer comprising monomeric units derived from olefins.

Polar: The term “polar” refers to a compound in which electrons are not equally shared between the atoms i.e., areas of positive and negative charges are permanently separated. A common example is water. Other polar compounds typically are soluble in water. In contrast, a nonpolar compound is one in which electrons are equally, or nearly equally, shared between the atoms. Common examples include fats and oils. Nonpolar compounds typically are insoluble in water.

Polymer: As used herein, the term “polymer” refers to a molecule of repeating structural or monomeric units bonded together or to a branched or hyperbranched core.

Polymerization: A chemical reaction, usually carried out with a catalyst, heat or light, in which a large number of relatively simple molecules (monomers) combine to form chainlike macromolecules (a polymer) where uniformity to non-uniformity of the chains is dependent on the reaction conditions, kinetics of the monomeric moieties, and/or polymerization technique employed. The monomers typically are unsaturated or otherwise reactive substances.

RAFT: Reversible addition-fragmentation chain transfer polymerization. RAFT is a reversible deactivation radical polymerization. RAFT is a controlled radical polymerization technique employed in the preparation of well-defined polymers. RAFT is performed with reagents that are capable of reversibly deactivating propagating radicals so that the majority of living chains are maintained in a dormant form, and under reaction conditions that support a rapid equilibrium between the active and dormant chains.

Viscosity index (VI): A measure of the change in kinematic viscosity with variations in temperature. A greater viscosity index indicates a smaller viscosity change with temperature. The temperatures used for reference are 40° C. and 100° C. As defined by the Society of Automotive Engineers, the original scale went from 0 (naphthenic oil) to 100 (best, paraffinic oil). Viscosity index improvers (VIIs) are additives that increase the viscosity index of an oil. Oils containing VIIs and synthetic oils may have a VI greater than 100. VI can be calculated using the formula VI=100×(L−U)/(L−H) where U is the kinematic viscosity (mm²/s) at 40° C., and L and Hare values based on the kinematic viscosity at 100° C. (available in ASTM D2270).

Weight Average Molecular Weight:

${Mw} = \frac{\Sigma \; N_{i}M_{i}^{2}}{\Sigma \; N_{i}M_{i}}$

where M_(i) is the molecular weight of a chain, and N_(i) is the number of chains of that molecular weight. Weight average molecular weight is determined by methods that are sensitive to molecular size, such as light-scattering techniques, small angle neutron scattering, X-ray scattering, and sedimentation velocity. When used in general statements (e.g., “comparable molecular weights”), the term “molecular weight” as used herein with respect to a polymer may refer to either of the number average molecular weight or the weight average molecular weight. When used in a specific context, the molecular weight is expressly stated as the number average or weight average molecular weight.

II. BRANCHED POLYMERS

FIG. 1 shows traditional schematic drawings of polymers with (a) linear, (b) ring, (c) star, (d) hyperbranched, and (e) dendrimer architectures. In general, as branching increases, viscosity influence decreases and shear robustness increases. Conventionally, a linear architecture with elastomeric features was used for viscosity modification of group I to group III oils. These earlier designs were prone to polymeric degradation caused by high shear forces within an internal combustion engine decreasing their effectiveness as viscosity modifiers. Branched architectures are more robust against shear degradation. However, rigid, highly branched structures modify the viscosity of solutions to a lesser extent than do their linear counterparts with similar molecular weights. Rigid and highly branched polymeric structures (i.e. dendrimers) undergo a minimal interaction, caused by chain entanglement, with one another in solution. In general, the average hydrodynamic volume ( V _(h)) of a non-linear polymer is smaller than its linear counterpart (i.e., a random coil) with a similar molecular weight in an ideal solvent. Overall, molecular weight and architecture influence the levels of chain entanglement and V _(h) at given concentrations, which contribute to the modification of lubricant viscosities when polymeric additives are employed.

Flexible branched or hyperbranched polymers in lubricant bases (e.g., oils) may improve the performance of lubricant formulations. In addition to improving the viscosity index of the lubricant, they may have longer life due to a structure that is more resistant to shear degradation than linear polymers, provide dynamic surface interaction via tailoring of peripherals and architecture, undergo a more significant change in V _(h) as related to changes in solubility governed by temperature, and/or limit increases to viscosity of the lubricant base at relatively low temperatures. Embodiments of the disclosed non-linear polymeric additives can increase lubricity by 1) mitigation of viscosity changes of lubricant bases over a range of temperatures and/or 2) reduction of friction in the boundary and mixed lubrication regimes at the contacting surface asperities. Viscosity index improvers (VII) generally include less soluble components for which overall solubility increases with temperature providing a more significant change in hydrodynamic volume ( V _(h)) from 40 to 100° C. VIIs are theorized to undergo a globular-to-coil transition due to their relatively lower shear thickening effect at lower temperatures, while reducing shear thinning at higher temperatures thereby providing competitive to superior viscosity index (VI) numbers. Depending on degree of branching, chemical composition, and/or polymer-solvent interaction, branched polymers may exist in a globular state that undergoes a significant conformational change dependent on temperature and solubility, making them useful as VIIs. FIG. 2 is a schematic diagram showing a conformational change of an exemplary branched polymer from a collapsed, globular conformation at cold temperatures to an expanded conformation at warmer temperatures. FIG. 3 is a schematic drawing showing intermolecular interactions between two exemplary branched polymers in an expanded conformation.

A. Hyperbranched Polymers

In some embodiments, a branched polymer lubricant additive is a hyperbranched polymer. The hyperbranched polymer may have a number average molecular weight M_(n) within a range of 50 to 500 kDa such as within a range of 50 to 400 kDa or 100 to 300 kDa, or 150 to 300 kDa. In one embodiment, the hyperbranched polymer comprises (i) a hyperbranched polar core having a functionality of at least 3 and comprising a plurality of heteroatoms and (ii) a plurality of arms bonded to the hyperbranched core molecule. In an independent embodiment, the hyperbranched polymer is a hyperbranched aryl polyester (HAPe) derived from AB₂ monomers, functionalized with lipophilic moieties, and having a comb-burst architecture. FIGS. 4A and 4B are schematic drawings of exemplary hyperbranched polymers that are subsequently functionalized with lipophilic or copolymeric moieties to form a branched polymer lubricant additive. FIG. 4A is post-modified dendrimer. FIG. 4B is a post-modified hyperbranched polymer, such as a HAPe.

1. Polymers with Hyperbranched Polar Cores

Some embodiments of the disclosed polymers comprise a hyperbranched polar core that includes a plurality of polar moieties and has a functionality of at least 3. In some embodiments, the hyperbranched polar core includes at least 50 carbon atoms, at least 75 carbon atoms, or at least 100 carbon atoms. Embodiments of the disclosed polar cores are derived from hyperbranched core molecules including a plurality of heteroatoms (e.g., oxygen, nitrogen) and at least 3 functional groups capable of reacting with a molecule having a complementary functional group. For example, a hydroxy or amino functional group may react with a carboxylic acid, an acyl halide, an alkyl ester, or an epoxide (e.g., an alkyl glycidyl ether). Suitable core molecules include, but are not limited to, bis(hydroxymethyl)propionic acid (bis-MPA) polyester analogs, branched polyethyleneimines (PEI), and branched polyamidoamine (PAMAM) dendrimers. In one embodiment, the core molecule is a bis-MPA polyester analog or a PAMAM dendrimer and includes from 8 to 256 functional moieties, such as from 8-128, 8-64, or 8-32 functional moieties. In some examples, the molecule includes 8, 16, 32, 64, 128, or 256 functional moieties. In an independent embodiment, the core molecule is a bis-MPA polyester analog or a PAMAM dendrimer that includes from 8 to 64 functional moieties, such as 8, 16, 32, or 64 functional moieties. In another embodiment, the core molecule is a PEI that includes from 8 to 260 functional moieties, such as from 8 to 150 functional moieties, or from 8 to 100 functional moieties.

Bis-MPA polyester analogs used as core molecules to form some embodiments of the disclosed branched polymers may have a functionality of 8-256, 8-128, 8-64, or 8-32, such as 8, 16, 32, 64, 128, or 256. Exemplary hyperbranched bis-MPA polyester-16-, 32-, and 64-hydroxyl analogs are shown below. In these exemplary structures, the core molecule has 3-4 main branches, which are further branched to provide the desired number of functional groups.

Exemplary branched polyethyleneimine core molecules used to form some embodiments of the disclosed branched polymers comprise primary, secondary, and tertiary amine groups. In some embodiments, the branched PEI molecules comprise primary, secondary, and tertiary amine groups in approximately a 25/50/25 ratio, and have a weight average molecular weight of 600-10,000 Daltons or 1,800-10,000 Daltons. In some embodiments, a PEI core molecule includes from 3 to 200 functional moieties (primary or secondary reactive amines). Because the structure is more variable than the dendritic polar cores, the functionality is an average. In one embodiment, a PEI core molecule with a weight average molecular weight of 600 Daltons has a functionality of 3.5. A representative structure where n is a positive integer is shown below:

Branched polyamidoamine (PAMAM) dendrimers used to form some embodiments of the disclosed branched polymers comprise primary, secondary and tertiary amine groups, and typically have an ethylenediamine or ammonia initiator core. Exemplary PAMAM core molecules have a primary amine functionality of 8-256, such as from 8-128, 8-64, or 8-32. In some examples, the primary amine functionality is 8, 16, 32, 64, 128, or 256. One representative PAMAM dendrimer with an ethylenediamine center and a functionality of 16 is shown below.

Hyperbranched polymers comprising a hyperbranched polar core have a plurality of polymeric or non-polymeric arms bonded to the functional groups of the polar core. In one embodiment, the branched polymer consists of a hyperbranched polar core and a plurality of polymeric or non-polymeric arms bonded to the functional groups of the polar core. The arms may be substantially nonpolar (i.e., lipophilic) or may include polar moieties. In some embodiments, an arm is bound to each functional group. However, it is possible that one or more functional groups on the hyperbranched polar core may remain unreacted, particularly if the polar core has a high functionality, e.g., a functionality >70. In certain embodiments, when the functionality is within a range of 3-21 and the plurality of arms is polymeric, the hyperbranched polar core is not a cyclotetrasiloxane derivative, a cyclophosphazene derivative, a calixarene derivative, a cyclodextrin derivative, or a saccharide derivative (e.g., an initiator based on a saccharide such as glucose or sucrose, e.g., penta(α-bromoisobutyryl)glucose, octa(α-bromo-isobutyryl)sucrose).

In one embodiment, a nonpolar arm is derived from a single molecule including a long (e.g., 8-20 carbon atoms) aliphatic chain, such as aliphatic carboxylic acids, aliphatic acyl halides, aliphatic esters, aliphatic glycidyl ethers, or any combination thereof. In one embodiment, the aliphatic group is unbranched. In an independent embodiment, the aliphatic group is unsubstituted. In certain non-limiting examples, the nonpolar arms are derived from stearic acid, dodecanoyl chloride, hexadecyl glycidyl ether, dodecyl methacrylate, or octadecyl methacrylate.

In another embodiment, nonpolar arms are polymers (homopolymers or copolymers) comprising monomeric units derived from nonpolar monomers. Suitable nonpolar monomers include, but are not limited to, alkenes, aryl-substituted alkenes, lipophilic vinyl monomers, long-chain aliphatic esters including a polymerizable double bond, such as alkyl methacrylates or alkyl acrylates wherein the alkyl group has 6 to 20 carbon atoms, such as 8-20 carbon atoms or 10-20 carbon atoms, and combinations thereof. In one embodiment, the nonpolar monomer is unbranched. In an independent embodiment, the alkene, aryl-substituted alkene, or aliphatic ester is unsubstituted. Exemplary nonpolar monomers include ethylene, styrene, dodecyl methacrylate, octadecyl methacrylate, and combinations thereof. The nonpolar polymeric arms may include an average of at least 50 monomeric units per arm, at least 100 monomeric units per arm, or at least 150 monomeric units per arm, such as from 50 to 300 monomeric units, from 100 to 300 monomeric units, or from 150 to 250 monomeric units. The arm length may be proportional to the size, molecular weight, and/or functionality of the core. As one non-limiting example, a core with a functionality of 8 may have polymeric arms comprising an average of at least 50 monomeric units, whereas a similar core with a functionality of 64 may have polymeric arms comprising an average of at least 100 monomeric units or at least 150 monomeric units. The number of monomers in individual polymeric arms may vary. Differing growth rates of the polymer may occur due, in part, to crowding as the polymer lengthens.

Nonpolar arms may fold or wrap around the hyperbranched polar core at lower temperatures, creating a globular conformation and increasing hydrophobicity by shielding the polar core. Desirably, the arms have a sufficient length to shield the polar core; hence a larger core may be functionalized with longer arms than a smaller core. At warmer temperatures, the nonpolar arms may unfold and extend into an expanded conformation, thereby increasing the hydrodynamic volume of the polymer, increasing intermolecular interactions between polymer molecules, and/or increasing polarity of the polymer by exposing the polar core. A lubricant including a hyperbranched polymer in an expanded conformation may exhibit increased viscosity compared to a lubricant that does not include a hyperbranched polymer.

In some embodiments, the arms include polar moieties. Arms including polar moieties may be copolymers comprising first monomeric units derived from nonpolar monomers and second monomeric units derived from polar monomers. The copolymers may be random copolymers or block or tapered block copolymers. In one embodiment, the block copolymer has a block of nonpolar monomeric units proximate the polar core and a block of polar monomeric units at distal ends of the arms. In an independent embodiment, the tapered block copolymer has a block of nonpolar monomeric units in a first portion of the arm proximate the polar core, a mixed block of nonpolar and polar monomeric units in a middle portion of the arm, and a block of primarily polar monomeric units at distal ends of the arms. If the nonpolar block proximate the core has a sufficient length, the arms may fold or wrap around the hyperbranched polar core at lower temperatures, creating a globular conformation and increasing hydrophobicity by shielding the polar core. The copolymers may include an average of at least 50 monomeric units per arm, at least 100 monomeric units per arm, or at least 150 monomeric units per arm, such as from 50 to 300 monomeric units, from 100 to 300 monomeric units, or from 150 to 250 monomeric units. The arm length may be proportional to the size, molecular weight, and/or functionality of the core. The copolymers may include an average of up to 50 mol % polar monomeric units, such as from 10-50 mol %, from 10-25 mol %, or from 10-20 mol % polar monomeric units. The number of monomeric units and the mol % of polar monomeric units may vary from arm to arm.

Suitable nonpolar monomers include, but are not limited to, alkenes, aryl-substituted alkenes, lipophilic vinyl monomers, and long-chain aliphatic esters including a polymerizable double bond, such as alkyl methacrylates or alkyl acrylates wherein the alkyl group has 6 to 20 carbon atoms, such as 8-20 carbon atoms or 10-20 carbon atoms, and combinations thereof. In one embodiment, the nonpolar monomer is unbranched. In an independent embodiment, the alkene, aryl-substituted alkene, or aliphatic ester is unsubstituted. Exemplary nonpolar monomers include ethylene, styrene, dodecyl methacrylate, octadecyl methacrylate, and combinations thereof.

In some embodiments, the polar monomers include at least one heteroatom. In certain embodiments, the polar monomers include at least one oxygen heteroatom, at least one nitrogen heteroatom, or at least one oxygen heteroatom and at least one nitrogen heteroatom. Suitable polar monomers include, but are not limited to, short-chain aliphatic esters, such as alkyl methacrylates wherein the alkyl group has 1-4 carbon atoms, and heteroaliphatic esters. Exemplary polar monomers include:

where t is an integer from 1 to 10, or any combination thereof.

2. Polymers with Hyperbranched Aryl Polyester (HAPe) Cores

In some embodiments, a hyperbranched polymer is prepared via polymerization of AB_(x) monomers, AB_(x)+B_(y) monomers, or A₂+B_(y) monomers (where A and B are functional groups, x≧2, y≧3) (Voit et al., Chem. Rev. 2009, 109:5924-5973). In some examples, x is 2, 3, or 4. In one embodiment, y is 3 or 4. An AB_(x) monomer is composed of two types of functional groups (A and B) that will exclusively react with one another. For example, an AB₂ monomer may have one carboxylate group and two hydroxy groups. Polymerization of an AB₂ monomer is a one-pot polymerization which encompasses step and chain growth synthetic approaches such as polycondensation, self-condensing vinyl polymerization (SCVP), and ring-opening multibranching polymerization (ROM-BP). An AB_(x)+B_(y) or A₂+B_(y) approach utilizes two monomers and produces a copolymer. In some embodiments, the branched polymer has a degree of branching within a range of 0.1 to 0.9, such as 0.1≦DOB<0.4 for a moderately branched polymer or 0.4≦DOB≦0.9 for a hyperbranched polymer, where 1 represents a dendrimer (maximum branching) and 0 represents the absence of branches.

In some embodiments, the resulting branched polymers include lipophilic oligomers within the core structure and peripheral hydroxy groups, which are post-modified with fatty acids to increase conformational changes and chain entanglement opportunities in the corona, as well as to modify the lipophilicity and therefore the solubility of the resulting compounds in base oils. Alternatively, the peripheral hydroxy groups are modified with moieties which may act as initiators towards a polymerization reaction, for example a bromoisobutyrate moiety. The branched core may then be further modified with polymeric arms starting from the appended initiators. The branched polymers may be a comb-burst hyperbranched aryl polyester (HAPe) with various internal and external lipophilic groups, molecular weights, and architectural features (e.g., degree of branching).

In some embodiments, the core is formed from an AB₂ monomer, wherein the AB₂ monomer is a methyl dihydroxybenzoate modified with an aliphatic alcohol or aliphatic silyl ether (e.g., an aliphatic tert-butyldimethylsilyl ether) to provide lipophilic oligomeric moieties terminating in a hydroxy group, thereby forming a monomer having the general structure:

where n is an integer from 3 to 20, such as from 3-18, 3-16, 3-12, 3-10, 4-10, or 4-6. The resulting branched polymer, following post-modification with lipophilic fatty acids, has a general structure with branching, linear, and terminal monomeric units as shown below:

where

represents a bond between monomers, m, o, and p are positive integers. In one embodiment, R is —C(O)—(CH₂)_(q)— and q is an integer from 8 to 16, such as from 10 to 14. In an independent embodiments, R is a polymeric arm as defined previously. The DOB may be from 0.1 to 0.9, such as 0.1≦DOB<0.4 for a branched polymer or from 0.4≦DOB≦0.9 for a hyperbranched polymer. In some embodiments with an AB₂ monomer, the DOB is 0.1-0.5. An exemplary polymer wherein n is 6, R is —C(O)—(CH₂)_(q)— and q is 14 (represented as “palm”) is shown in FIG. 5.

In one embodiment, the branched polymer consists of an aryl polyester core derived from AB_(x) monomers, AB_(x)+B_(y) monomers, or A₂+B_(y) monomers, where x≧2 and y≧3, the aryl polyester core having a degree of branching from 0.1 to 0.9, and a plurality of polymeric or non-polymeric arms bonded to the aryl polyester core. In an independent embodiment, the branched polymer consists of an aryl polyester core derived from AB₂ monomers, the aryl polyester core having a degree of branching from 0.1 to 0.9 or from 0.1 to 0.5, and a plurality of polymeric or non-polymeric arms bonded to the aryl polyester core.

B. Branched Polyolefins

In some embodiments, a branched polymer lubricant additive is a branched polyolefin comprising first monomeric units derived from an olefin and second monomeric units derived from ene-containing polar monomers (polar monomers including an alkenyl functional group), including but not limited to vinyl monomers, acrylate monomers, methacrylate monomers, and combinations thereof. Desirably the olefin and polar monomers are monofunctional monomers that include only one polymerizable double bond. In some embodiments, the second monomeric units comprise at least one heteroatom such as an oxygen atom, at least one nitrogen atom, or at least one oxygen atom and at least one nitrogen atom. In one embodiment, the branched polymer is a branched polyolefin consisting of first monomeric units derived from an olefin and second monomeric units derived from ene-containing polar monomers.

A branched polyolefin may have a hyperbranched or moderately branched topology, depending at least in part on the pressure under which it was synthesized. In some examples, polyethylene synthesized at a pressure of 15 psi has a hyperbranched topology, whereas polyethylene synthesized at a pressure of 100 psi has a moderately branched topology (FIG. 6). Synthesis temperature also may affect the degree of branching, with higher temperatures increasing the degree of branching.

A moderately branched polyolefin may have a greater viscosity index than a comparable (e.g., similar molecular weight and polarity) hyperbranched polyolefin. The moderately branched polyolefin may have a globular configuration when included in a lubricant at low temperatures (e.g., −20 to 40° C.). At higher temperatures (e.g., 40 to 150° C.), the moderately branched polyolefin may uncoil into an expanded configuration, thereby increasing viscosity of the lubricant compared to the viscosity of the lubricant in the absence of the moderately branched polyolefin.

The olefin may be any aliphatic, acyclic hydrocarbon comprising one or more double bonds. In some embodiments, the olefin has a single double bond. Suitable olefins include, but are not limited to, C₂-C₁₂ aliphatic alkenes, such as C₂-C₈ or C₂-C₄ aliphatic alkenes (e.g., ethene (ethylene), propene, 1-butene, 2-butene), and combinations thereof.

Suitable polar monomers may include (i) a polymerizable double bond at or near a first end of the molecule (e.g., between C1 and C2 or between C2 and C3) and (2) at least one heteroatom, such as at least one oxygen heteroatom, at least one nitrogen heteroatom, or at least one oxygen heteroatom and at least one nitrogen heteroatom, near (e.g., within 2-4 atoms of) the terminal end of the molecule. In some embodiments, the polar monomers are esters. Exemplary polar ester monomers include, but are not limited to, esters having a general formula R¹—C(O)O—R², wherein R¹ is an alkenyl moiety and R² is a short-chain alkyl moiety (e.g., 1-3 carbon atoms) or a heteroaliphatic moiety including at least one oxygen atom, at least one nitrogen atom, or at least one oxygen atom and at least one nitrogen atom. R¹ may be a branched or unbranched alkenyl moiety. For example, R¹ may be H₂C═C(H)—(CH₂)_(z)— or H₂C═C(CH₃)—(CH₂)_(z)— where z is an integer from 0-20. In certain examples, the polar monomers are C₁-C₃ alkyl esters of unsaturated carboxylic acids having a double bond between C1 and C2 or between C2 and C3 (e.g., methyl-9-decenoate, ethyl-9-decenoate, methyl-9-undecenoate, methyl-10-undecenoate, ethyl-10-undecenoate, methyl-11-dodecenoate, etc.),

where t is an integer from 1 to 10, or a combination thereof. In one embodiment, when the olefin is ethylene, the polar monomers are not an alkenyl ether, methyl-9-decenoate or methyl 2,2-dimethylpent-4-enoate.

The branched polyolefin may include from 0.5 to 25 mol % monomeric units derived from polar monomers, such as from 0.5 to 10 mol %, 0.5 to 5 mol %, or 1 mol % to 3 mol % monomeric units derived from polar monomers, with the remaining monomeric units derived from nonpolar alkene monomers. In one embodiment, the branched polyolefin is a random copolymer. In an independent embodiment, the branched polyolefin is a block copolymer, such as a block copolymer wherein the polar monomers are added after polymerization of the nonpolar alkene monomers to provide polar monomers at the terminal ends of the polymer branches.

In some embodiments, the branched polyolefin has a number average molecular weight M_(n) within a range of 50-300 kDa, such as within a range of 50-200 kDa, 50-100 kDa or 50-75 kDa. In one embodiment, the branched polyolefin is a moderately branched polymer having a degree of branching within a range of 30 to 90 branching points per 1000 carbons, such as from 80 to 90 branching points per 1000 carbons. In an independent embodiment, the branched polyolefin is a hyperbranched polymer having a degree of branching within a range of 90 to 200 branching points per 1000 carbons, such as from 100 to 120 branches per 1000 carbons.

Embodiments of branched polyolefins comprising both polar and nonpolar monomeric units have a lower viscosity in oil at room temperature than a comparably sized and branched polyolefin comprising only nonpolar monomeric units. For example, as shown in Example 2, branched polyolefins prepared from 98 mol % ethylene monomers and 2 mol % methyl-10-undecenoate monomers had a room temperature kinematic viscosity in a group III oil at 2 wt % that was 30-70% lower than the room temperature viscosity of 1.67 wt % of Control 2 in the group III oil. Advantageously, branched polyolefins comprising both polar and nonpolar monomeric units also provide substantial friction reduction when added to an oil at low concentrations, e.g., from 1 to 5 wt %, such as from 1-3 wt %. For example, as shown in Example 2 and FIGS. 13-14, the branched polyolefins prepared from 98 mol % ethylene monomers and 2 mol % methyl-10-undecenoate monomers reduced the kinetic coefficient of friction in a group I oil by up to 45% at temperatures ranging from 23° C. to 100° C.

III. LUBRICANTS AND METHODS OF USING THE LUBRICANTS

Embodiments of the disclosed branched polymers are useful as additives in lubricant compositions, such as in engine oils, gear oils, air compressor oils, transformer oils, hydraulic oils, drill oils, turbine oils, and other lubricant compositions. In some embodiments, a lubricant includes an embodiment of a branched polymer as disclosed herein and a base oil selected from American Petroleum Institute (API) group I (less than 90% saturates, greater than 0.03% sulfur, and a VI of 80-120), group II (more than 90% saturates, less than 0.03% sulfur, and a VI of 80-120), group III (more than 90% saturates, less than 0.03% sulfur, and a VI greater than 120), group IV (synthetic, polyalphaolefin), and group V oils (silicones, phosphate esters, polyalkylene glycols, polyolester, etc.).

In some embodiments, the lubricant includes an amount of the branched polymer sufficient to provide the lubricant with a viscosity index ≧150, such as a VI within a range of 150-250. In some embodiments, the VI is ≧170 or ≧190, such as within a range of 170-250 or 190-250. The amount of the branched polymer may be a concentration within a range of 1 to 50 wt %, such as 1 to 25 wt %, 1 to 10 wt %, 1 to 5 wt %, 2 to 5 wt %, or 1 to 3 wt %.

In some embodiments, the lubricant has a coefficient of friction that is at least 10%, at least 20%, at least 30%, or at least 40% less than the coefficient of the lubricant base alone in contact with a component of a device during operation of the device at a temperature within a range of 20 to 100° C. In certain embodiments, the coefficient of friction is reduced by 5-50% throughout the temperature range of 20 to 100° C. A moderately branched or hyperbranched polymer has significantly more end-groups than conventional lubricants, such as linear polymers, leading to increased interaction with the surface or other polar moieties on the surface and reduced friction of the lubricant. Thus, embodiments of the disclosed branched polymers may reduce or eliminate the need for additional friction-reducing additives in the lubricant.

In some embodiments, a lubricant including a branched polymer as described herein improves fuel efficiency of light- and medium-duty vehicles by at least 1%, such as by at least 2%, without adverse impacts on other vehicle performance parameters or durability.

The lubricant may include other additives as are known to one of ordinary skill in the art of lubricant formulations. Other additives may include, for example, detergent additives, corrosion or rust-inhibiting additives, antioxidant additives, metal deactivators, pour point depressants, extreme pressure agents, antiwear additives, dispersants, antifoam agents, antimisting agents, friction modifiers, additional viscosity index improvers, additional viscosity modifiers, and combinations thereof.

Embodiments of the disclosed lubricants are useful for lubricating a device, particularly a mechanical device. The lubricant may reduce wear and tear (e.g., due to friction) of a component of the device during operation of the device. The device is lubricated by supplying to the device a lubricant as disclosed herein. Exemplary devices include, but are not limited to, engines, gears, air compressors, transformers hydraulic devices, drills, and turbines. In one embodiment, the device is an engine.

IV. BRANCHED POLYMER SYNTHESIS A. Hyperbranched Polymers Having a Hyperbranched Polar Core

In some embodiments, a hyperbranched polar core is commercially available. For example, hyperbranched bis-MPA polyester-16-, 32-, and 64-hydroxyl analogs, branched polyethyleneimine cores, and branched polyamidoamine (PAMAM) dendrimer cores are commercially available. In other embodiments, a hyperbranched polar core may be synthesized. A plurality of “arms” is added to the hyperbranched polar core.

In some embodiments, the arms are substantially nonpolar and are derived from aliphatic carboxylic acids, aliphatic acyl halides, aliphatic esters, aliphatic glycidyl ethers, nonpolar polymeric arms or any combination thereof. In one example, a polyethyleneimine core is dissolved in a suitable solvent (e.g., tetrahydrofuran) under an inert atmosphere, and then reacted with a long-chain acyl halide (e.g., dodecanoyl chloride) under suitable conditions (e.g., at room temperature, in the presence of an amine such as triethanolamine) for an effective period of time, such as for 8-18 hours. In another embodiment, a polyethyleneimine core is dissolved in a suitable solvent under an inert atmosphere, and then reacted with an aliphatic glycidyl ether (e.g., glycidyl hexadecyl ether) under suitable conditions (e.g., at room temperature, in the presence of water) for an effective period of time, such as for 8-18 hours. In yet another embodiment, a PAMAM core is dissolved in a suitable solvent under an inert atmosphere, and then reacted with an aliphatic glycidyl ether (e.g., glycidyl hexadecyl ether) under suitable conditions (e.g., at room temperature, in the presence of water) for an effective period of time, such as for 8-18 hours. The modified hyperbranched polymer may be purified by dissolving the polymer in a suitable solvent (e.g., dichloromethane) and precipitation (e.g., into cold diethyl ether).

In certain embodiments, the arms are homopolymers comprising monomeric units derived from nonpolar monomers or copolymers comprising first monomeric units derived from nonpolar monomers and second monomeric units derived from polar monomers. Atom-transfer radical polymerization (ATRP) is used to grow the arms on the hyperbranched polar core. The core is first functionalized, e.g., as shown in FIG. 7 with an exemplary PEI core. The functionalized core is then combined with monomers to grow polymeric arms by ATRP, RAFT, or free radical polymerization. In some embodiments, the functionalized core is combined with monomers and a suitable catalyst, e.g., a copper catalyst, to grow polymeric arms by ATRP. ATRP may provide a narrower molecular weight distribution than RAFT or free radical polymerization.

B. Hyperbranched Aryl Polyesters

Embodiments of the disclosed hyperbranched aryl polyesters are synthesized from AB_(x) monomers. The polymer may be post-modified, e.g., with fatty acids, to add lipophilic groups.

One exemplary synthetic scheme is shown in FIG. 8. An AB_(x) monomer may be initially modified to include a lipophilic oligomer having a “B” functional group. For example, methyl 3,5-dihydroxybenzoate may be modified with 6-bromo-1-hexanol or 8-bromo-1-octanol to produce methyl 3,5-bis((8-hydroxyhexyl)oxy)benzoate or methyl 3,5-bis((8-hydroxyoctyl)oxy)benzoate, respectively.

The oligomer-modified monomer is then polymerized to form a hyperbranched polymer. The oligomer-modified monomer is dissolved in a suitable solvent and a polymerization initiator is added. In some examples, the initiator is an organotin initiator, such as dibutyltin diacetate. The reaction is allowed to proceed at an effective temperature for an effective amount of time to provide a hyperbranched polymer. In some embodiments, the effective temperature is from 160-200° C., such as 180° C. The reaction may proceed until the monomer is substantially consumed and/or a polymer of the desired molecular weight is obtained. Monomer consumption and molecular weight may be monitored, for example, by thin layer chromatography and NMR spectroscopy. The polymer may be purified by dilution in a suitable solvent followed by precipitation.

The hyperbranched polymer is then post-modified to introduce lipophilic groups at the branch termini. In some embodiments, the lipophilic groups are provided by reaction with acyl halide derivatives of fatty acids, e.g., C₁₀-C₂₀ fatty acids. The hyperbranched polymer is dissolved in a suitable solvent under an inert atmosphere. A long-chain aliphatic acyl halide (e.g., dodecanoyl chloride) is added to the hyperbranched polymer and allowed to react under suitable conditions (e.g., at room temperature, in the presence of an amine such as trimethyl amine or another HCl scavenger) for an effective period of time. The post-modified hyperbranched polymer may be purified by dissolving the polymer in a suitable solvent followed by precipitation.

C. Branched Polyolefins

Embodiments of the disclosed branched polyolefins are synthesized in a pressurized vessel. A solvent and a suitable catalyst (e.g., a palladium catalyst) are added to the vessel. Two exemplary Pd catalysts are shown:

The vessel is sealed and purged with the selected olefin until a desired pressure is attained. In some embodiments, the desired pressure is from 1-150 psi (6.9-1035 kPa), such as from 15-100 psi (100-700 kPa). The pressure may be selected, in part, based on a desired degree of branching in the polyolefin. In some embodiments, pressures at the low end of the range produce a hyperbranched polymer whereas pressures at the high end of the range produce a moderately branched polymer (see, e.g., Wang et al., Ind. Eng. Chem. Res. 2007, 46:1174-1178). As the olefin polymerizes, the pressure within the sealed vessel drops. Periodically, the vessel is recharged with additional olefin. The reaction may be allowed to proceed until no further pressure drop occurs.

In some embodiments, the branched polyolefin is a copolymer including a polar co-monomer. The co-monomer can be added simultaneously with the olefin to produce a random copolymer. Alternatively, the co-monomer can be added near the end of the synthesis, thereby producing a block or tapered block copolymer wherein monomeric units derived from the co-monomer are selectively located at or near the terminal ends of the branches.

Following synthesis, a resinous product is recovered. The resin is redissolved in a suitable solvent (e.g., diethyl ether) and washed. In some examples, the resin is washed with dilute acid, such as 2 M HCl. After removal of the aqueous phase, hydrogen peroxide is added to the resin and allowed to react for an effective period of time to remove traces of the catalyst from the branched polyolefin. The reaction then is quenched, e.g., by adding ice. The product is washed and dried. Removal of volatiles produces a viscous oil comprising the branched polyolefin.

V. EXAMPLES General

Anhydrous solvents from septum sealed bottles were used as received to run reactions, while reagent grade solvents were utilized for transfers and purification of products. Reactants and catalyst were used as received from suppliers. Triethylamine (TEA) was dried over activated molecular sieves (4 Å) prior to use. Anhydrous reaction glassware and equipment was oven dried and cooled under vacuum. These reaction vessels were backfilled with argon flowing through a tube filled with activated silica gel orange (drying agent). Thin layer chromatography (TLC; Baker-flex® precoated flexible sheets) was used as needed to monitor reactions. UV lamp and TLC staining agents (i.e., KMnO₄) were employed to identify spots of interest. A group I oil (unadditized) from ExxonMobil and a group III oil (4 Yubase unadditized) were used as is to create a baseline data set for viscosity and friction measurements, clean between measurements, and prepare weight concentrations of polymer in base oil. Control 1 and Control 2 are commonly utilized proprietary lubricant viscosity modifiers or viscosity index improvers, employed here as comparative models and were kindly donated by industry partners. Control 1 is a proprietary hydrocarbon polymer with a trade name of OS#198530A (Lubrizol Corporation, Wickliffe, Ohio). Control 2 is Viscoplex® 6-850, a proprietary product (Evonik Industries AG, Essen, Germany).

Characterization:

Nuclear magnetic resonance spectroscopy (NMR) was utilized to confirm the chemical composition of monomers and polymers. Samples were dissolved in deuterated chloroform (CDCl₃) containing tetramethylsilane (TMS, 0.3-1%, v/v). The proton (¹H) and carbon (¹³C) spectra were captured on a Varian 500 MHz instrument. TMS (δ=0.00) and CDCl₃ (δ=7.26 (¹H), 77.16 (¹³C)) were used as internal references for ¹H NMR and ¹³C NMR respectively. Peaks were identified as singlets (s), doublets (d), triplets (t), multiplets (m), and broad (b). Integration was utilized to determine relative number of protons within the sample. Small molecule samples (i.e., monomers) were submitted for time of flight mass spectrometry (TOF-MS) analysis. Data is reported below. Polymers were subjected to size exclusion chromatography (SEC) analysis which was conducted in THF and the molar mass determined against polystyrene standards.

Lubricant Investigations:

Polymers were mixed into group I or III oil at concentrations of 1-3 wt %. Heat (50-120° C.) and agitation had to be employed to produce homogeneous blends. Several samples would become turbid and precipitate out at temperatures below 50° C. This required additional agitation prior to viscosity and friction measurements. Dynamic viscosity was measured with several instruments, depending on the needs and temperature and shear range of the instrument. The viscosity data was recorded in centipoise (cP) and converted into centistokes (cSt) by dividing the centipoise value by the density of the blend. The densities of the blends were the same irrespective of the polymer contained therein. A Brookfield viscometer was equipped with a cooling/heating jacket that was continuously flowing with oil supplied by an external cooling/heating bath that regulated the temperature at 40 and 100° C. A rotating spindle (0.3-100 rpm) was submerged into the blended oil at the regulated temperatures and the dynamic shear was reported on the digital screen with a respective torsion percent. The cP value with the highest torsion percent was used for viscosity index calculations. Viscosity was measured by the dropping ball or a Viscolite® 700 (VL7-100B-HP) viscometer at 10 and 23° C. A Tannas TBS viscometer was utilized to measure the viscosity of the blended oils at 150° C. while under a shear rate of 1×10⁶ s⁻¹. A reference oil (R-350, 2.617 cP at 150° C.) was utilized to calibrate the instrument with a specific spindle height as well as provide a linear slope (RPM vs. shear rate) to interpolate the viscosities of the blended oils. A variable load-speed bearing tester (VLBT) was utilized to measure friction coefficients (Blau et al., Wear 2013, 302(1-2):1064-1072). The load was applied through a stiff spring that was compressed by a ball screw at the end of the load arm. A 25.4 mm square coupon of A2 tool steel was used to press against a 25.4 mm diameter rotating steel bar of AISI 8620 alloy steel. A cartridge heater was installed under the coupon holder to control the temperature. The oil was supplied at the beginning of each test by filling the coupon holder. A 50 N normal load was applied for tests at 23° C. and a 26 N normal load was applied for those at 100° C. The speed cycle was in 0.1 m/s steps between 1.7 m/s and 0.2 m/s. The period for each step was 10 seconds. There were 3 cycles tested for each sample for a total of 480 seconds. The friction coefficients for the same speed from the 2^(nd) and the 3^(rd) cycle were averaged and plotted while the 1^(st) cycle served as the running-in period with its data unused. Between each test, the tested oil was removed and the coupon and the bar were cleaned using isopropyl alcohol. A pin-on-disk tribometer (CSM Instruments) may be used for wear evaluation screening.

Example 1 Hyperbranched Aryl Polyesters Monomer Synthesis (AB₂) (Saha et al., Macromolecules 2008, 41(15):5658-5664):

Methyl 3,5-bis((8-hydroxyhexyl)oxy)benzoate (n=4)

Methyl 3,5-dihydroxybenzoate (5.88 g, 0.035 mol), potassium carbonate (48.02 g, 0.35 mol), potassium iodide (˜0.1 g), and 18-crown-6 (˜0.025 g) were transferred into a 2-neck round bottom flask fitted with a condenser while under positive argon flow. The reaction flask was then degassed and left under vacuum for ca. 30 minutes. The reaction flask was backfilled with argon and left under an argon-inflated balloon. Acetonitrile (˜300 mL) was transferred into the reaction flask via cannula and positive argon pressure. While stirring the mixture, 6-bromo-1-hexanol (13.94 g, 0.076 mol, ˜2.2 equivalents) was added via syringe. The reaction was then heated until a medium reflux was achieved. In ca. 12 hours the reaction mixture turned brown and TLC analysis indicated the consumption of benzoate (5% MeOH/DCM; UV active). The insoluble species were removed by filtration, the filtrate was collected and the volatile organics were removed via roto-evaporation. The crude oil was re-dissolved in EtOAc (500 mL) and washed against 1 N HCl (500 mL) by agitating the biphasic layers in a separatory funnel. Fresh EtOAc (250 mL) and aqueous layer were agitated and separated three more times. The combined organic extracts were dried over anhydrous sodium sulfate, the solvent was removed, the residue dried and a viscous, amber color, oil was isolated (quantitatively) and analyzed by TLC, NMR, and MS. TLC (5% MeOH/DCM; UV): R_(f)=0.30 (major), 0.32 (minor). ¹H NMR (CDCl₃, 500 MHz): δ 7.16 (s, 2H), 6.63 (s, 1H), 3.98 (t, 4H, J=5 Hz), 3.90 (s, 3H), 3.66 (t, 4H, J=5 Hz), 1.80 (m, 4H), 1.61 (m, 4H), 1.55-1.36 (b, 10H). ¹³C NMR (CDCl₃, 125 MHz): δ 167.10, 160.21, 131.96, 107.78, 106.73, 68.27, 62.98, 52.34, 32.77, 29.24, 25.97, 25.63. HRMS (ESI): m/z 391.2079 (MNa⁺, [C₂₀H₃₂O₆]Na⁺ requires 391.2097 g/mol).

Methyl 3,5-bis((8-hydroxyoctyl)oxy)benzoate (n=6)

This monomer was prepared as described above with the exception of utilizing 8-bromo-1-octanol (˜2.1 eq.). A yellow-orange viscous oil was isolated (quantitatively) and analyzed by TLC, NMR, and MS. TLC (5% MeOH/DCM; UV): R_(f)=0.30 (major), 0.32 (minor). ¹H NMR (CDCl₃, 500 MHz): δ 7.16 (s, 2H), 6.63 (s, 1H), 3.97 (t, 4H, J=5 Hz), 3.90 (s, 3H), 3.65 (t, 4H, 5 Hz), 1.78 (m, 4H), 1.58 (m, 4H), 1.46 (m, 4H), 1.41-1.29 (b, 14H). ¹³C NMR (CDCl₃, 125 MHz): δ 167.14, 160.23, 95.46, 68.37, 63.15, 52.35, 32.86, 29.42, 26.05, 25.78. HRMS (ESI): m/z 447.2724 (MNa⁺, [C₂₄H₄₀O₆]Na⁺ requires 447.2723 g/mol).

Polymerization Procedure (Hawker et al., Macromolecules 1996, 29(11):3831-3838).

Typical Procedure:

Without further purification, methyl 3,5-bis((8-hydroxyhexyl)oxy)-benzoate (n=4), obtained as described above, was dissolved in anhydrous dichlorobenzene (DCB) to a concentration of 1.0 M and kept under positive argon pressure. The reaction was fitted with a straight condenser and streaming N₂ was used to continuously clear the head space. The reaction vessel was heated to 120° C. and then 1-3 drops of initiator, (n-Bu)₂Sn(OAc)₂, was added. The exterior temperature was then increased to 180° C. Once TLC analysis indicated the majority of monomer was consumed, the reaction was subsequently followed by ¹H NMR spectroscopy. Once the DP corresponded to a molecular weight of interest, the reaction mixture was removed from the heating mantle and allowed to cool to room temperature. Bubbling nitrogen through the crude solution removed the majority of DCB. The remaining viscous oil was diluted in DCM and precipitated into cold Et₂O (−40° C.). The precipitate isolated from vacuum filtration was collected and placed under high vacuum for ca. 16 hours, to obtain an amber viscous oil in yields greater than 50%.

HAPe1 ( DP 37, M _(n)=124 kDa). ¹H NMR (CDCl₃, 500 MHz): δ 7.15 (s, 2.11H), 6.62 (s, 1.00H), 4.30 (s, 2.06H), 3.97 (s, 3.61 H), 3.89 (s, 0.14H), 3.65 (s, 1.48H), 1.79 (s, 7.39H), 1.71-1.31 (b, 11.18H).

HAPe2 ( DP=29, M _(n)=11.5 kDa). ¹H NMR (CDCl₃, 500 MHz): δ 7.14 (s, 2.01H), 6.61 (s, 1.00H), 4.28 (t, 1.96H, J=5 Hz), 3.95 (t, 4.09H, J=5 Hz), 3.88 (s, 0.10H), 3.63 (b, 2.35H), 1.81-1.68 (b, 7.10H), 1.61 1.50 (b, 3.16H), 1.50 1.40 (b, 7.08H), 1.40-1.29 (b, 11.84).

Post-modification of HAPes (Sunder et al., Angew. Chem. Int. Ed. 1999, 38(23):3552-3555).

Typical Procedure:

HAPe1 (˜3.89 g; DP=37, M _(n)=12.4 kDa) was dissolved in anhydrous THF (20 mL) and transferred into a 2-neck reaction flask. The flask was placed into an ice bath (0° C.) for ca. 15 minutes. While under an argon balloon, Et₃N (ca. 2 eq.) was injected into the flask. Dodecanoyl chloride (C12, ca. 2 eq.) was added slowly to the mixture via syringe. The reaction was allowed to warm to room temperature and stirred overnight. The resulting ammonium salt was removed by vacuum filtration and rinsed with THF. The filtrate and wash were collected, combined and concentrated to 10 mL volume via roto-evaporation. MeOH (˜5 mL) was added to the crude mixture to quench remaining acyl chlorides and stirred for 20 minutes, followed by solvent removal. The resulting waxy material was re-dissolved in DCM and the concentrated polymer solution was precipitated into cold Et₂O (−40° C.). The precipitate was collected via vacuum filtration. This purification was repeated once more and the resulting residue dried under vacuum for ca. 16 hours. A waxy white solid was collected with a typical gravimetric yield of ca. 50%.

HAPe1+C12 (1; DP=15, M _(n)=8.13 kDa). ¹H NMR (CDCl₃, 500 MHz): δ 7.14 (s, 2.05H), 6.61 (s, 1.00H), 4.29 (b, 1.88H), 4.06 (b, 2.53H), 3.95 (b, 4.55H), 3.88 (s, 0.21 H), 2.27 (m, 1.41H), 1.7-1.55 (b, 5.27H), 1.55-1.36 (b, 10.80H), 1.34-1.15 (b, 14.70H), 0.86 (b, 2.62H). SEC (PS cal.): M _(n) ^(app)=17.1 kg/mol, M _(w) ^(app)=55.7 kg/mol, D_(M)=3.3, multimodal.

HAPe1+C16 (2; DP=15, M _(n)=8.83 kDa). ¹H NMR (CDCl₃, 500 MHz): δ 7.14 (s, 2.02H), 6.60 (s, 1.00H), 4.29 (b, 2.06H), 4.05 (b, 2.55H), 3.95 (b, 4.32H), 3.87 (s, 0.20H), 2.27 (b, 1.48H), 1.78 (b, 7.41), 1.71-1.55 (b, 5.89H), 1.55-1.44 (b, 7.55H), 1.44-1.37 (b, 3.84H), 1.32-1.17 (b, 24.25H), 0.85 (b, 2.68H). ¹³C NMR (CDCl₃, 125 MHz): δ 174.01, 171.23, 166.50, 160.08, 132.19, 107.70, 106.20, 70.85, 68.10, 65.12, 64.22, 34.41, 31.98, 29.74, 29.21, 28.70, 25.84, 25.06, 22.76, 21.06, 14.21. SEC (PS cal.): M _(n) ^(app)=18.2 kg/mol, M _(w) ^(app)=52.8 kg/mol, D_(M)=2.9, multimodal.

HAPe2+C12 (3; DP=26, M _(n)=15.3 kDa). ¹H NMR (CDCl₃, 500 MHz): δ 7.14 (s, 2.16H), 6.61 (s, 1.00H), 4.28 (t, 1.95H, J=5 Hz), 4.05 (t, 2.40H, J=5 Hz), 3.95 (m, 5.46H), 3.88 (s, 0.12H), 2.28 (m, 2.25H), 1.77 (m, 8.88H), 1.61 (s, 5.58), 1.52-1.16 (m, 78.86H), 0.87 (m, 10.23H). ¹³C NMR (CDCl₃, 125 MHz): δ 174.17, 169.97, 166.67, 160.19, 145.67, 132.30, 107.73, 106.25, 101.88, 68.34, 65.34, 64.46, 53.84, 34.53, 32.04, 31.09, 29.73, 29.45, 28.78, 27.63, 26.47, 26.09, 25.15, 24.77, 22.82, 14.27. SEC (PS cal.): M _(n) ^(app)=14.7 kg/mol, M _(w) ^(app)=25.9 kg/mol, D_(M)=1.7, multimodal.

HAPe2+C16 (4; DP=26, M _(n)=17.6 kDa). ¹H NMR (CDCl₃, 500 MHz): δ 7.14 (s, 2.31 H), 6.61 (s, 1.00H), 4.28 (t, 2.10H, J=5 Hz), 4.05 (t, 2.78H, J=5 Hz), 3.95 (m, 6.25H), 3.88 (s, 0.13H), 2.29 (m, 3.27H), 1.76 (s, 11.07), 1.61 (s, 9.73H), 1.52-1.13 (m, 156.60H), 0.87 (t, 12.62H, J=5 Hz). ¹³C NMR (CDCl₃, 125 MHz): δ 174.50, 169.94, 166.65, 160.18, 145.67, 132.29, 107.72, 106.23, 101.85, 68.32, 65.33, 64.44, 53.83, 51.57, 34.51, 34.24, 32.06, 29.80, 29.61, 29.50, 29.40, 29.32, 28.77, 26.46, 26.08, 25.14, 24.76, 22.83, 14.26. SEC (PS cal.): M _(n) ^(app)=15.1 kg/mol, M _(w) ^(app)=25.7 kg/mol, D_(M)=1.7, multimodal.

Results and Discussion

Four derivatives of hyperbranched aryl polyesters (HAPe) were prepared. The derivatives included variation of the lipophilic linkage of the monomer by six or eight carbons and the modification of the subsequent polymer with long chain acyl chlorides (dodecanoyl chloride, C12, or palmitoyl chloride, C16), to afford saturated fatty esters in the corona (FIG. 8, Scheme 1). The three-step synthesis included a quantitative preparation of the monomer, a gravimetric yield greater than 50% of the alcohol-functionalized polymerization product, followed by a variable yield (49% to quantitative) post-functionalization of the peripheral alcohols into fatty esters. Over-polymerization (leading to an insoluble gel) occurred quite readily. To mitigate the over-polymerization of the analog, as well as reduce the average degree of branching, the monomer was diluted in dichlorobenzene (DCB). Thus a 1.0 M solution of the monomer was heated near reflux and treated with a tin catalyst (n-Bu₂SnOAc₂) to initiate polymerization. The polymerization was monitored closely by ¹H NMR to prevent the formation of an insoluble resin which appeared to occur with relatively high average degree of polymerizations ( DP). The polymerization was monitored by ¹H NMR over 6 hours, which was generally the time required to achieve a soluble polymer. A broadening and slow disappearance of the methyl ester peak at 3.88 ppm was closely monitored and utilized in conjunction with the ether methylene peak at 3.95 ppm to target DPs between 10 and 30. As is the case with step-growth polymerizations, the relationship of the conversion of the monomer into polymer with molecular weight was non-linear. Therefore, the determination of DP via an aliquot removed from the reaction mixture and measured by ¹H NMR did not provide accurate insight into the progression of the polymerization in regards to molecular weight. To determine number-average molecular weight ( M _(n)) via ¹H NMR spectroscopy, analogs 1, 2, 3, and 4 were first purified by precipitation. Polymerizations 5, 6, and 7 were terminated by simply adding the next step reagents, i.e. palmitoyl chloride (C16) and triethyl amine (TEA). Analogs 1, 2, 3, and 4 were subsequently treated with either dodecanoyl chloride (C12) or C16 and TEA in tetrahydrofuran (THF). All analogs were then purified via precipitation techniques prior to further characterization.

Characterization: The polymers were analyzed by nuclear magnetic resonance (NMR) spectroscopy to determine M _(n) and chemical composition (i.e. percent of post-functionalization, P_(f)%). The M _(n) values were found to range from 3.05 to 34.5 kg/mol (Table 1). The P_(f)% was determined to be between 49 to 99%. The apparent number-average molecular weights ( M _(n) ^(app)) and molar dispersity (D_(M)) were determined to be between 4.75-18.2 kg/mol and 1.55-3.27, respectively, by size exclusion chromatography (SEC). There are discrepancies between ¹H NMR and SEC M _(n) values suggesting an error in calculating DP via end group analysis or the hydrodynamic volume of polymers with comparable molar masses have significantly different architectures (linear vs. dendritic) thereby influencing the elution volume. For example, analogs 1 and 2 were determined by end group analysis to have M _(n) values approximately half of analogs 3 and 4. However, SEC suggests the reverse understanding with analogs 1 and 2 having M _(n) ^(app) values greater than analogs 3 and 4. Complications in obtaining accurate molar masses from ¹H NMR are due to increasing peak overlap between the broadening methylene ether (δ=3.95) and gradual disappearance of the methyl ester (δ=3.88) protons. However, the broad (D_(M)<3.3) and multi-modal spectra obtained from SEC also limit accurate interpretation of how the hydrodynamic volume (V_(h)) may be related to architectural or molecular weight differences. The elucidation of the architectural differences of these polymeric samples, by determining the average degree of branching ( DB) via NMR spectroscopy, was not possible. Similar systems consist of aromatic protons which are close to the alcohol/ester functionality in the polymer and therefore respond to those respective environmental changes in the molecule (Wooley et al., Polym. J. 1994, 26(2):187-197; Shu et al., Macromolecules 1999, 32(1):100105). The DB can be determined from integration of the phenyl protons. With these analogs, however, all functional groups that undergo a change are six or eight carbons away from the phenyl ring, and thus the aromatic protons do not “see” a responsiveness to these changes. Although the branched structure was unable to be confirmed by NMR analysis, the AB₂ polycondensation reaction is well-known to produce hyperbranched architectures.

TABLE 1 ¹H NMR^(b) SEC^(d) Ana- M _(n) M _(n) ^(app) M _(w) ^(app) log Composition^(a) DP ^(c) P_(f) %^(c) R ^(c) (kg/mol)^(c) (kg/mol) (kg/mol)

1 HAPe1 + C12 16 98 17  8.3 17.1 55.7 3.3  5.2 + (3.1) 2 HAPe1 + C16 16 98 19  9.86 18.2 52.8 2.9 5.36 + (4.5) 3 HAPe2 + C12 26 89 28 15.3 14.7 25.9 1.7 10.2 + (5.1) 4 HAPe2 + C16 26 66 31 17.6 15.1 25.7 1.7 10.2 + (7.4) 5 HAPe2 + C16 6 49 3  3.05 4.75 7.35 1.6 2.35 + (0.7) 6 HAPe2 + C16 46 >99 50 29.9 6.1 17 2.8  18.0 + (11.9) 7 HAPe2 + C16 <56 96 53 34.5 9.86 26.5 2.7  21.9 + (12.6) ^(a)HAPe1 (n = 4) and HAPe2 (n = 6) were subjected to post-modification with palmitoyl chloride (C16) or dodecanoyl chloride (C12); ^(b)Nuclear magnetic resonance (NMR) spectrometry with tetramethylsilane (TMS, δ = 0.00) as an internal reference for proton (¹H) analysis in deuterated chloroform (CDCl₃); ^(c)see below for details on calculations of average degree of polymerization ( D.P), percent of post-functionalization (P_(f) %), average number of peripheral groups ( R), and number-average molecular weight ( M _(n)); ^(d)apparent number-average molecular weight ( M _(n) ^(app)) and molar dispersity 

 were determined by utilizing polystyrene standards via size exclusion chromatography (SEC) analysis.

The average degree of polymerization ( DP= m+ō+ p) was calculated using the integration of the protons associated with the methyl ester (δ=3.88; and the methylene peaks of the alkyl aryl ether (δ=3.95; 4.5513H/4H=1.1378; 1.1378/0.07326=15.5). The number average molecular weight ( M _(n)) was calculated by multiplying DP (15.5) by repeating unit molar masses (HAPe1=335.42 g/mol×15.5=5209 g/mol). The conversion of terminal alcohols into esters was determined by dividing the integration of the ester methylene peak (δ=4.06; 2.5353H) by the sum of the integration of the methylene peaks adjacent to the ester and unreacted alcohol (δ=3.65; 0.0352H+2.5353H=2.5705H; 2.5353H/2.5705H=0.986×100%=98.6%). The number of alcohols post-modified into fatty esters was determined by dividing the normalized integration of the sum of methylene next to ester and methylene next to alcohol (2.5705H/2H=1.285) to the normalized integration of the methyl (1.285/0.07326=17.5). This value was multiplied by the percent of post-functionalization (P_(f)%; 17.5×98.6%=17.29). The molecular weight contribution of the fatty esters was calculated by multiplying R by the molecular weight of C12 (183.32 g/mol×17.29=3171 g/mol) or C16 (239.42 g/mol).

Viscosity Analysis: The performance of these polymers/oligomers as viscosity index improvers was evaluated. In addition, the relatively high density of heteroatoms was expected to increase the interaction with the metal surfaces, thereby reducing friction near the boundary regime. The molecular feature that is responsible for friction reduction can result in a reduced lipophilicity and therefore solubility in base oils. Additional heating (≧50° C.) was used to prepare homogeneous blends which underwent a reversible phase separation at temperatures <50° C. The polymers were mixed in group I oil (ExxonMobil) at concentrations of 1-3 wt % via agitation and heating. Blends of Controls 1 and 2 were prepared at the appropriate concentrations and utilized as comparative model systems due to their prevalence as viscosity modifiers within the lubricant field. In order to calculate the viscosity index of the additives, the dynamic viscosity (centipoise; cP) of the 2 wt % blends was measured at 40 and 100° C. utilizing a rotary spindle viscometer. Kinematic viscosity values, in centistokes (cSt), were calculated from these numbers and are reported in Table 2 at a 2 wt % concentration. Viscosity indices (VI) were calculated (www.uniteasy.com/en/unitsCon/calvi.htm). Another significant value for lubricant evaluation and the subsequent determination of the oil grade it falls in (http://www.sae.org), is a high temperature high shear test (HTHS), which imposes a low viscosity limit on the final oil (Covitch et al., SAE Int'l J. of Fuels and Lubricants 2010, 3(2):1030-1040). This test was performed at 150° C. which is presumed to be approaching the highest temperature and shear boundary the lubricant may experience during engine operation (ASTM DS-62).

TABLE 2 Dropping Ball Spindle HTHS Viscometer (cSt)^(d) Viscometer (cSt)^(d) (cSt)^(d,f) Analog 10° C. 23° C. 40° C. 100° C. VI 150° C. Group I^(a) n.d.^(e) n.d. 31.4 5.3 97 2.3 Control 1^(b) 1053  430  311.5 40.1 182 4.7 Control 2^(c) 229 106  89.8 15.1 178 2.6 1 152 67 31.5 5.3 99 n.d. 2 153 67 31.7 5.4 105 n.d. 3 n.d. n.d. 31.9 5.4 104 n.d. 4 n.d. n.d. 31.6 5.3 101 2.4 5 n.d. n.d. 30.9 5.2 94 n.d. 6 157 71 32.4 5.4 99 n.d. 7 156 69 32.1 5.4 101 n.d. ^(a)Group I oil density = 0.84 g/cm³; ^(b)VII additized (2 wt % polymer) group I oil density = 0.86 g/cm³; ^(c)Control 2 corrected wt % is 1.67; ^(d)cSt = cP/p; ^(d)not determined (n.d.); ^(e)high temperature and high shear (HTHS) was performed according to ASTM D4683.

For comparison of kinematic viscosity values and the respective VIs, of the controls, base oil and the comb-burst analogs, the results are illustrated in a bar graph (FIG. 9). The ideal lubricant formulation would be homogeneous and undergo little viscosity change over a wide range of temperatures. Control 1 and 2, in group I oil, were homogeneous over a wide range of temperatures (10 to 100° C.). However, Control 1 significantly increased the viscosity of the neat oil from 31.4 cSt to 311.5 cSt at 40° C. Furthermore, Control 1 demonstrated an undesirable increase in viscosity at 10° C. (1053 cSt) which may lead to problematic engine cold-starts, particularly in colder climates.

The viscosity index values reflect the overall resistance to the natural thinning tendency of lubricants and provide a unit-less number to compare one lubricant formulation to another. In general, a high viscosity index value with little effect on viscosity of the lubricant at lower temperatures is desirable.

Lubricant formulations prepared with a 2 wt % concentration of the synthesized polymeric additives, HAPe, demonstrated little influence as a VM or VII. Little to no increase in viscosity was observed at 40° C., which is desirable, while at 100° C. no increase in viscosity was observed with respect to the group I oil, which is undesirable. As a result, the VIs of the HAPe lubricant formulations were below those of the controls. Furthermore, there was no clear connection between molecular weight and/or architecture, and viscosity results. For example, analog 2 ( M _(n)=8.83 kg/mol) results suggested a small increase in viscosity from the neat group I oil at 40 and 100° C. (31.4→31.7 and 5.3→5.4 cSt, respectively) providing a slightly elevated VI of 105. Analog 4 ( M _(n)=17.6 kg/mol) results indicated a slightly lower increase in viscosity (31.4→31.6 and 5.3→5.3 cSt, respectively) and VI (101). However, the changes in viscosity and respective VIs were within standard error and therefore did not provide insight into whether the suspected architectural differences might be influencing lubricant performance or not. In any case, the HAPe additives demonstrated little influence on the bulk oil's viscosity.

Viscosity is a fluid's ability to resist shear. For practical use, oils must meet the requirements set out in SAE engine oil viscosity classification J300 (http://www.sae.org). This includes low and high temperature viscometry, as well as a high shear rate requirement of 1×10⁶ s⁻¹ at 150° C. High shear rate analysis under high temperature conditions provides insight into how a lubricant formulation may hold up in real world applications. The neat group I oil, Controls 1 and 2, and analog 4 viscosities were measured at 150° C. and a shear rate of 1×10⁶ s⁻¹ to evaluate performance of these lubricant formulations under limiting conditions. The viscosities of group I oil (2.3 cSt) and analog 4 (2.4 cSt) were ca. 44% of their respective viscosities at 100° C. Controls 1 (4.7 cSt) and 2 (2.6 cSt) demonstrated a more significant loss in viscosity under these conditions, respectively ca. 12% and 17% of their original viscosities at 100° C. A comparable loss in viscosity for the controls can be observed from 40 to 100° C., suggesting that the differences observed could be attributed to the natural thinning effect of the lubricant formulation and not to the failure of the additive at high shear rates. Interestingly, although analog 4 had very little effect as a VI improver, the viscosity under these extreme conditions was actually higher than that of the oil. It can be postulated that the retention of viscosity was due to the hyperbranched topology of the analog.

FIG. 10 shows a Stribeck Curve and illustrations of boundary lubrication, mixed lubrication, and hydrodynamic lubrication regimes (Rivzi, Lubricant Chemistry, Technology, Selection, and Design, ASTM International, West Coshohocken, P A 2009, page 657). Friction coefficients (μ) against speed (m/s) were measured at room temperature (−23° C.) and 100° C. on a variable-load journal bearing tester (VLBT), for lubricant formulations of Control 2 and analog 2. In FIGS. 11A-11C, the friction trace of neat group I base oil was an average of two baseline tests performed before and after, each additized oil was tested.

In FIG. 11A, at 23° C. (left panel), Control 2 at a concentration of 1.67 wt % appeared to have no influence on the friction versus the neat oil. At 100° C. (right panel), a reduction in μ was observed over the entire range. The gains in reducing friction at higher temperatures may be due to the benefit of a higher viscosity of Control 2 (15.1 cSt at 100° C.) versus the neat oil (5.3 cSt at 100° C.). It is well accepted that a thicker lubricant will possess reduced friction versus a thin lubricant under identical conditions. In FIG. 11B, at both 23 and 100° C., analog 2 at a concentration of 2 wt % showed a significant friction reduction in mixed and boundary lubrication at speeds <0.7 m/s. The observed reduction in friction may be attributed to a layer of polymeric additive deposited on the contact surfaces. This was not observed in the case of Control 2, where Control 2 has a more favorable viscosity than analog 2 (vide infra) and therefore should have a lower friction by default. It is conceivable that a thin polymeric film is formed at the interface, which lowers the coefficient of friction. The differences in viscosity between Control 2 (106 cSt at 23° C.; 15.1 cSt at 100° C.) and analog 2 (67 cSt at 23° C.; 5.4 cSt at 100° C.) made it challenging to compare these two formulations directly. In FIG. 11C, the friction reduction of each additized oil was calculated by subtracting its friction trace from that of the base oil. At 23° C. (left panel), the more significant friction reduction in mixed and boundary lubrication regimes was produced by the lower-viscosity analog 2-additized oil compared with the Control 2-additized oil; at 100° C. (right panel), such reduction was only observed on the transition from boundary regime to mixed regime at ˜0.5 m/s.

Example 2 Branched Polyethylenes

The polymerization procedure was conducted in Parr apparatus that was dried and then backfilled with argon. Dichloromethane was transferred into the system via cannula (50 mL), followed by the addition of the Pd catalyst in dichloromethane (0.1 M, 0.1 mL).

The apparatus was sealed and purged with ethylene until a pressure of 100 psi was reached. As the reaction proceeded, the pressure decreased. The apparatus was recharged with ethylene up to 100 psi 2-3 times through the course of 2 days until no further consumption of ethylene was observed, producing a branched polyethylene with moderately branched topology. In another example, the polymerization procedure was performed at 15 psi, resulting in a hyperbranched topology according to literature precedents.

At that point the reaction was worked up as follows. The volatiles were removed under reduced pressure until a resin was obtained. The resin was redissolved in ether and washed with 2M HCl. After the aqueous phase was removed, 10 mL of 30% H₂O₂ were added and the resulting mixture was allowed to stir at room temperature overnight to remove the Pd catalyst from the polymer. The next day the reaction was quenched with ice. The mixture washed with saturated NaHCO₃, followed by 1M HCl, and then dried over Na₂SO₄. Removal of volatiles resulted in a viscous oil that was readily oil soluble.

When a co-monomer is used, the co-monomer can be added at the beginning of the reaction around the same time as ethylene is added, or at the end of the reaction. The proof of concept trials used ethylene. However the synthesis is not limited to any particular alkenes.

Example 2-1

Using the above procedure, 13.3 g of branched polyethylene homopolymer final product was obtained (analog 9). Another polyethylene homopolymer was synthesized at 10-15 psi (analog 8).

Example 2-2

Branched polyethylene was synthesized at 100 psi. Methyl 10-undecenoate was added after ethylene consumption was complete, and the reaction was allowed to proceed at atmospheric pressure for two additional days. The amount of methyl-10-undecenoate was sufficient to provide a concentration of 2 mol % in the polymer. The yield of the final product (analog 10) was 12.7 g.

Example 2-3

Methyl 10-undecenoate (2 mol %) was added together with the first charge of ethylene. The synthesis was carried out at 100 psi. The reaction yielded 10.8 g of product (analog 11).

The number average molecular weight M_(n) was determined to be 67.5 kDa for the homopolymers (8, 9) and 65.5 kDa for the copolymers (10, 11). All analogs were miscible in a group III base oil (YUBASE-4). Viscosity was measured at 40 and 100° C., and the viscosity index was determined (FIG. 12). All four analogs outperformed Control 1 as viscosity index improvers. The inclusion of the polar co-monomer had little or no influence on VI, but had a significant influence on room temperature viscosity. Room temperature kinematic viscosity was 159 cSt for analog 9, 106 cSt for analog 10, and 53 cSt for analog 11. The viscosity index values were 186 for analog 9, 179 for analog 10, and 176 for analog 11.

Friction performance at 23° C. and 100° C. was assessed using a group I base oil (EMG1). Control 2 was added to the base oil at a concentration of 1.67 wt %. Analogs 9, 10, and 11 were evaluated at a concentration of 2 wt %. Variable load-speed bearing tester was used: 50 N load, 8620 steel bar against A2 steel flat, 23° C., 1.6-0.2 m/s speed range. The results are shown in FIGS. 13A-13D (23° C.) and 14A-14D (100° C.). Control 2 had little to no influence on friction (FIGS. 13A, 14A). Inclusion of the polar co-monomer (analogs 10 and 11, FIGS. 13C, 14C and 13D, 14D, respectively) provided substantial friction reduction. Overall, analog 10, a block copolymer, had the lowest viscosity and the highest reduction in friction, indicating that a single material can act as both a viscosity and friction modifier.

In view of the many possible embodiments to which the principles of the disclosed invention may be applied, it should be recognized that the illustrated embodiments are only preferred examples of the invention and should not be taken as limiting the scope of the invention. Rather, the scope of the invention is defined by the following claims. We therefore claim as our invention all that comes within the scope and spirit of these claims. 

We claim:
 1. A branched polymer, comprising: (a) a hyperbranched polar core having a functionality of at least 3 and comprising a plurality of heteroatoms, and a plurality of polymeric or non-polymeric arms bonded to the hyperbranched polar core, wherein when the functionality is within a range of 3-21 and the plurality of arms is polymeric, the hyperbranched polar core is not a cyclotetrasiloxane derivative, a cyclophosphazene derivative, a calixarene derivative, a cyclodextrin derivative, or a saccharide derivative; (b) an aryl polyester core derived from AB_(x) monomers, AB_(x)+B_(y) monomers, or A₂+B_(y) monomers, where x≧2 and y≧3, the aryl polyester core having a degree of branching within a range of 0.1 to 0.9, and a plurality of polymeric or non-polymeric arms bonded to the aryl polyester core; or (c) a branched polyolefin including first monomeric units derived from an olefin and second monomeric units derived from polar monomers, each polar monomer including at least one heteroatom, wherein when the olefin is ethylene, the polar monomers are not an alkenyl ether, methyl-9-decenoate, or methyl 2,2-dimethylpent-4-enoate.
 2. The branched polymer of claim 1, wherein the branched polymer comprises a hyperbranched polar core derived from: a branched 2,2-bis(hydroxymethyl)propionic acid polyester comprising 8-256 hydroxy moieties; a branched polyethyleneimine comprising primary, secondary, and tertiary amine groups and having an weight average molecular weight within a range of 600-10,000 Daltons; or a branched polyamidoamine comprising 8-256 primary amine moieties.
 3. The branched polymer of claim 2, wherein each of the plurality of arms is a non-polymeric arm derived from a C₈-C₂₀ aliphatic carboxylic acid, a C₈-C₂₀ aliphatic acyl halide, a C₈-C₂₀ aliphatic ester, or a C₈-C₂₀ aliphatic glycidyl ether.
 4. The branched polymer of claim 2, wherein each of the plurality of arms is a random copolymer or a block copolymer, the random or block copolymer comprising first monomeric units derived from nonpolar monomers and second monomeric units derived from polar monomers.
 5. The branched polymer of claim 4, wherein the nonpolar monomers are unsubstituted alkenes, aryl-substituted alkenes wherein the aryl group is alkyl-substituted or unsubstituted, alkyl acrylates wherein the alkyl group of the alkyl acrylate is unsubstituted and has 6 to 20 carbon atoms, methacrylates wherein the alkyl group of the alkyl methacrylate is unsubstituted and has 6 to 20 carbon atoms, lipophilic vinyl monomers, or a combination thereof.
 6. The branched polymer of claim 4, wherein each of the second monomeric units comprises at least one heteroatom.
 7. The branched polymer of claim 4, wherein the polar monomers are

where t is an integer from 1 to 10, or a combination thereof.
 8. The branched polymer of claim 1, wherein the branched polymer comprises: an aryl polyester core derived from AB₂ monomers having a structure

where n is an integer from 3 to 20, and the core has a degree of branching within a range of 0.1 to 0.9.
 9. The branched polymer of claim 8, comprising a plurality of non-polymeric arms having a structure

where q is an integer from 8 to
 16. 10. The branched polymer of claim 9, comprising a plurality of homopolymeric arms derived from a nonpolar monomer, wherein the nonpolar monomer is an unsubstituted alkene, an aryl-substituted alkene wherein the aryl group is alkyl-substituted or unsubstituted, an alkyl acrylate wherein the alkyl group of the alkyl acrylate is unsubstituted and has 6 to 20 carbon atoms, a methacrylate wherein the alkyl group of the alkyl methacrylate is unsubstituted and has 6 to 20 carbon atoms, or a lipophilic vinyl monomer.
 11. The branched polymer of claim 9, comprising a plurality of copolymeric arms comprising first monomeric units derived from nonpolar monomers and second monomeric units derived from polar monomers, each second monomeric unit comprising at least one heteroatom.
 12. The branched polymer of claim 11, wherein the first monomeric units are derived from ethylene and the second monomeric units are derived from polar monomers having a general formula R¹—C(O)O—R², wherein R¹ is an alkenyl moiety and R² is a C₁-C₃ alkyl moiety or a heteroaliphatic moiety including at least one oxygen atom, at least one nitrogen atom, or at least one oxygen atom and at least one nitrogen atom.
 13. The branched polymer of claim 12, wherein the polar monomers are

where t is an integer from 1 to 10, or a combination thereof.
 14. The branched polymer of claim 1, wherein the branched polymer is a branched polyolefin and the polar monomers comprise vinyl monomers, acrylate monomers, methacrylate monomers, or a combination thereof.
 15. A lubricant, comprising: a lubricant base; and a branched polymer that, when combined with a lubricant base at a concentration from 1 wt % to 50 wt %, (i) provides a viscosity index 150, (ii) has a coefficient of friction that is at least 10% less than a coefficient of friction of the lubricant base alone in contact with a component of a device during operation of the device at a temperature within a range of 20 to 100° C., or (iii) both (i) and (ii), wherein the branched polymer is (a) a branched polymer comprising (i) a hyperbranched polar core having a functionality of at least 3 and comprising a plurality of heteroatoms, and (ii) a plurality of polymeric or non-polymeric arms bonded to the hyperbranched polar core, wherein when the functionality is within a range of 3-21 and the plurality of arms is polymeric, the hyperbranched polar core is not a cyclotetrasiloxane derivative, a cyclophosphazene derivative, a calixarene derivative, a cyclodextrin derivative, or a saccharide derivative; (b) a branched polymer comprising an aryl polyester core derived from AB_(x) monomers, AB_(x)+B_(y) monomers, or A₂+B_(y) monomers, where x≧2 and y≧3, the aryl polyester core having a degree of branching within a range of 0.1 to 0.9, and a plurality of polymeric or non-polymeric arms bonded to the aryl polyester core; or (c) a branched polyolefin comprising first monomeric units derived from an olefin and second monomeric units derived from a polar monomer including at least one heteroatom.
 16. The lubricant of claim 15, comprising 1 to 50 wt % of the branched polymer.
 17. The lubricant of claim 15, wherein the lubricant base is a group I oil, group II oil, a group III oil, a group IV oil, a group V oil, or any combination thereof.
 18. A method for making a lubricant, comprising: combining a lubricant base with a branched polymer to form a lubricant having (i) a viscosity index ≧150, (ii) has a coefficient of friction that is at least 10% less than a coefficient of friction of the lubricant base alone in contact with a component of a device during operation of the device at a temperature within a range of 20 to 100° C., or (iii) both (i) and (ii), wherein the branched polymer is (a) a hyperbranched polymer comprising (i) a hyperbranched polar core having a functionality of at least 3 and comprising a plurality of heteroatoms, and (ii) a plurality of polymeric or non-polymeric arms bonded to the hyperbranched polar core, wherein when the functionality is within a range of 3-21 and the plurality of arms is polymeric, the hyperbranched polar core is not a cyclotetrasiloxane derivative, a cyclophosphazene derivative, a calixarene derivative, a cyclodextrin derivative, or a saccharide derivative; (b) a branched polymer comprising an aryl polyester core derived from AB_(x) monomers, AB_(x)+B_(y) monomers, or A₂+B_(y) monomers, where x≧2 and y≧3, the aryl polyester core having a degree of branching within a range of 0.1 to 0.9, and a plurality of polymeric or non-polymeric arms bonded to the aryl polyester core; or a branched polyolefin comprising first monomeric units derived from an olefin and second monomeric units derived from a polar monomer including at least one heteroatom.
 19. The method of claim 18, wherein the lubricant has a concentration of the branched polymer within a range of 1-50 wt %.
 20. A method for lubricating an engine, comprising supplying to the engine a lubricant according to claim
 15. 